online phd in applied mathematics

Applied Mathematics (Ph.D.)

Applied mathematics addresses problems in science, engineering, and society. Find new ways to solve real-world problems through original, creative research in Illinois Tech’s applied mathematics Ph.D. program.

Academic Programs

Illinois Tech’s Ph.D. program in Applied Mathematics is a flagship graduate program that prepares talented mathematicians and statisticians for careers in research or academia through a rigorous education, which includes advanced coursework, independent study, and original research. With almost 100 percent job placement at graduation, our alumni work at Goldman Sacks, UBS, Amazon, University of Michigan, DePaul University, United Airlines, Grant Thornton, as well as start-ups and early stage companies.

The Department of Applied Mathematics and the College of Computing offer generous scholarships in the form of teaching or research assistantships that cover tuition and provide a competitive monthly stipend.

Courses cover a wide range of topics in applied mathematics and statistics including mathematical courses offered in popular graduate programs such as Data Science , Financial Technology , and Computational Decision Science and Operations Research .

The Department of Applied Mathematics is a vibrant research hub with internationally recognized faculty working in a variety of applied research areas such as computational mathematics, stochastic analysis, statistics, data science, applied discrete mathematics, and optimal control.

In addition to numerous academic activities, the Department of Applied Mathematics is home to several student organizations such as Illinois Tech SIAM Student Chapter, American Statistical Association, Association for Women in Mathematics, Machine Learning @IIT, and Fun Math Problems.

Program Overview

Prepare for a career in industrial research or academia through a rigorous education that includes advanced coursework, independent study, and original research to make a significant contribution to the field of applied mathematics.

Career Opportunities

Career opportunities exist across industries, as so many need mathematics experts.

Operations researcher/analyst
Mathematician/statistician
Post-secondary mathematics/science teacher
Post-secondary mathematics/science administrator

View Details

Admission Requirements

The program typically requires a bachelor’s degree in mathematics or applied mathematics. Candidates whose degree is in another field and whose background in mathematics is strong are also eligible for admission and are encouraged to apply.

Applicants should have a bachelor’s degree from an accredited university. A cumulative GPA of 3.5/4.0 is usually required.

TOEFL scores, if required, should be a minimum of 80/550 (internet-based/paper-based test scores).

A two-page professional statement of goals/objectives and a curriculum vitae must be submitted.

Three letters of recommendation are required.

All applications are automatically considered for full scholarship in from of Teaching or Research Assistantship, with no additional application process for such funds. The scholarships are awarded to top candidates based on the strength of the entire portfolio, the departmental needs and the availability of funds. Full consideration are given to applications for Fall semesters received before the priority deadline of January 31.

Ask a Professor

What do climate change, finance, data science, sports analytics, engineering, and software development all have in common? They all have foundations in mathematics. Discover how a degree in applied mathematics can open doors to these careers, and many more, by speaking with Professor Igor Cialenco, director of graduate studies at Illinois Tech’s Department of Applied Mathematics. These virtual visits occur on Wednesdays from 3 p.m. to 4 p.m. CST.

Featured Faculty

Igor Cialenco

Jinqiao (Jeffrey) Duan

Sonja Petrović

Fred J. Hickernell

Maggie Cheng

Our alumni hit the ground running

By planning together, the Department of Applied Mathematics and Jeffery Mudrock forged a plan allowing him to work full-time while pursuing a Ph.D. and his career goals.

Learning experiences from a network of collaborators helped Lluís Antoni Jiménez Rugama evaluate mathematics from a variety of perspectives.

After emigrating to the United States, Kabre ran her own business before pursuing a Ph.D. in applied mathematics and a career in academia.

Yicong Huang finds himself incorporating his research experience into his daily work.

With a combination of theoretical and practical research experience, Xiao Huang can’t find a work problem he is unable to solve.

Learn more...

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PhD in Applied Mathematics and Statistics

Create knowledge at the nation’s leading research institution. Our doctoral program in applied mathematics and statistics prepares you for leadership, no matter what professional path you choose.

With an emphasis on mathematical reasoning, mathematical modeling and computation, interdisciplinary, and the development of new methodology, the department’s doctoral program produces graduates with broad expertise, who have worked in cutting-edge advances in applied mathematics and statistics, and who are prepared to pursue careers in academia, industry, the public sector, and more.

Research and academic opportunities in the doctoral program cover a wide range of interconnected areas within applied mathematics that reflect the department faculty’s diverse scientific interests. These include:

Data Science with a focus on theoretical foundations, modeling techniques, and algorithm development.
Probability and statistics with a focus both on theory and applications, particularly related to machine learning.
Financial mathematics , as well as a concentration in optimization/operations research, which address discrete and continuous optimization problems.
Discrete mathematics , with a focus on combinatorics and graph theory.
Computational and applied mathematics , with a focus on the development of mathematical and numerical models for various applications in fluid dynamics, shape analysis and biomedical engineering.

Ph.D. Student Handbook

Explore your options

Pursue a PhD with a focus on computational medicine

Doctoral candidates can focus their studies on computational medicine, through a partnership with JHU’s Institute for Computational Medicine, a collaboration between JHU’s School of Engineering and the renowned School of Medicine.

A commitment to discovery

Connecting the Dots - Carey Priebe has worked with hospitals hoping to reduce stress on surgical nurses, shown how satellites can spot Martian volcanoes, and given law enforcement new tools against human traffickers, shadowy financial networks, and corporate fraud.

NSF Program Support Career-readiness for Graduate Students - To help prepare graduate students in the mathematical sciences for careers in business, industry, and government, the Johns Hopkins Engineering and the University of Illinois at Urbana-Champaign are partnering to create the Internship Network in the Mathematical Sciences (INMAS).

$NYU Courant Department of Mathematics$

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Ph.D. in Atmosphere Ocean Science
M.S. at Graduate School of Arts & Science
M.S. at Tandon School of Engineering
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Ph.D. in Mathematics, Specializing in Applied Math

Table of contents, overview of applied mathematics at the courant institute.

PhD Study in Applied Mathematics
Applied math courses

Applied mathematics has long had a central role at the Courant Institute, and roughly half of all our PhD's in Mathematics are in some applied field. There are a large number of applied fields that are the subject of research. These include:

Atmosphere and Ocean Science
Biology, including biophysics, biological fluid dynamics, theoretical neuroscience, physiology, cellular biomechanics
Computational Science, including computational fluid dynamics, adaptive mesh algorithms, analysis-based fast methods, computational electromagnetics, optimization, methods for stochastic systems.
Data Science
Financial Mathematics
Fluid Dynamics, including geophysical flows, biophysical flows, fluid-structure interactions, complex fluids.
Materials Science, including micromagnetics, surface growth, variational methods,
Stochastic Processes, including statistical mechanics, Monte-Carlo methods, rare events, molecular dynamics

PhD study in Applied Mathematics

PhD training in applied mathematics at Courant focuses on a broad and deep mathematical background, techniques of applied mathematics, computational methods, and specific application areas. Descriptions of several applied-math graduate courses are given below.

Numerical analysis is the foundation of applied mathematics, and all PhD students in the field should take the Numerical Methods I and II classes in their first year, unless they have taken an equivalent two-semester PhD-level graduate course in numerical computing/analysis at another institution. Afterwards, students can take a number of more advanced and specialized courses, some of which are detailed below. Important theoretical foundations for applied math are covered in the following courses: (1) Linear Algebra I and II, (2) Intro to PDEs, (3) Methods of Applied Math, and (4) Applied Stochastic Analysis. It is advised that students take these courses in their first year or two.

A list of the current research interests of individual faculty is available on the Math research page.

Courses in Applied Mathematics

The following list is for AY 2023/2024:

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(MATH-GA.2701) Methods Of Applied Math

Fall 2023, Oliver Buhler

Description: This is a first-year course for all incoming PhD and Masters students interested in pursuing research in applied mathematics. It provides a concise and self-contained introduction to advanced mathematical methods, especially in the asymptotic analysis of differential equations. Topics include scaling, perturbation methods, multi-scale asymptotics, transform methods, geometric wave theory, and calculus of variations.

Prerequisites : Elementary linear algebra, ordinary differential equations; at least an undergraduate course on partial differential equations is strongly recommended.

(MATH-GA.2704) Applied Stochastic Analysis

Spring 2024, Jonathan Weare

This is a graduate class that will introduce the major topics in stochastic analysis from an applied mathematics perspective. Topics to be covered include Markov chains, stochastic processes, stochastic differential equations, numerical algorithms, and asymptotics. It will pay particular attention to the connection between stochastic processes and PDEs, as well as to physical principles and applications. The class will attempt to strike a balance between rigour and heuristic arguments: it will assume that students have some familiarity with measure theory and analysis and will make occasional reference to these, but many results will be derived through other arguments. The target audience is PhD students in applied mathematics, who need to become familiar with the tools or use them in their research.

Prerequisites: Basic Probability (or equivalent masters-level probability course), Linear Algebra (graduate course), and (beginning graduate-level) knowledge of ODEs, PDEs, and analysis.

(MATH-GA.2010/ CSCI-GA.2420) Numerical Methods I

Fall 2023, Benjamin Peherstorfer

Description: This course is part of a two-course series meant to introduce graduate students in mathematics to the fundamentals of numerical mathematics (but any Ph.D. student seriously interested in applied mathematics should take it). It will be a demanding course covering a broad range of topics. There will be extensive homework assignments involving a mix of theory and computational experiments, and an in-class final. Topics covered in the class include floating-point arithmetic, solving large linear systems, eigenvalue problems, interpolation and quadrature (approximation theory), nonlinear systems of equations, linear and nonlinear least squares, and nonlinear optimization, and iterative methods. This course will not cover differential equations, which form the core of the second part of this series, Numerical Methods II.

Prerequisites: A good background in linear algebra, and some experience with writing computer programs (in MATLAB, Python or another language).

(MATH-GA.2020 / CSCI-GA.2421) Numerical Methods II

Spring 2024, Aleksandar Donev

This course (3pts) will cover fundamental methods that are essential for the numerical solution of differential equations. It is intended for students familiar with ODE and PDE and interested in numerical computing; computer programming assignments in MATLAB/Python will form an essential part of the course. The course will introduce students to numerical methods for (approximately in this order):

The Fast Fourier Transform and pseudo-spectral methods for PDEs in periodic domains
Ordinary differential equations, explicit and implicit Runge-Kutta and multistep methods, IMEX methods, exponential integrators, convergence and stability
Finite difference/element, spectral, and integral equation methods for elliptic BVPs (Poisson)
Finite difference/element methods for parabolic (diffusion/heat eq.) PDEs (diffusion/heat)
Finite difference/volume methods for hyperbolic (advection and wave eqs.) PDEs (advection, wave if time permits).

Prerequisites

This course requires Numerical Methods I or equivalent graduate course in numerical analysis (as approved by instructor), preferably with a grade of B+ or higher.

( MATH-GA.2011 / CSCI-GA 2945) Computational Methods For PDE

Fall 2023, Aleksandar Donev & Georg Stadler

This course follows on Numerical Methods II and covers theoretical and practical aspects of advanced computational methods for the numerical solution of partial differential equations. The first part will focus on finite element methods (FEMs), and the second part on finite volume methods (FVMs) including discontinuous Galerkin (FE+FV) methods. In addition to setting up the numerical and functional analysis theory behind these methods, the course will also illustrate how these methods can be implemented and used in practice for solving partial differential equations in two and three dimensions. Example PDEs will include the Poisson equation, linear elasticity, advection-diffusion(-reaction) equations, the shallow-water equations, the incompressible Navier-Stokes equation, and others if time permits. Students will complete a final project that includes using, developing, and/or implementing state-of-the-art solvers.

In the Fall of 2023, Georg Stadler will teach the first half of this course and cover FEMs, and Aleks Donev will teach in the second half of the course and cover FVMs.

A graduate-level PDE course, Numerical Methods II (or equivalent, with approval of syllabus by instructor(s)), and programming experience.

Elman, Silvester, and Wathen: Finite Elements and Fast Iterative Solvers , Oxford University Press, 2014.
Farrell: Finite Element Methods for PDEs , lecture notes, 2021.
Hundsdorfer & Verwer: Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations , Springer-Verlag, 2003.
Leveque: Finite Volume Methods for Hyperbolic Problems , Cambridge Press, 2002.

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( MATH-GA.2012 ) Immersed Boundary Method For Fluid-Structure Interaction

Not offered AY 23/24.

The immersed boundary (IB) method is a general framework for the computer simulation of flows with immersed elastic boundaries and/or complicated geometry. It was originally developed to study the fluid dynamics of heart valves, and it has since been applied to a wide variety of problems in biofluid dynamics, such as wave propagation in the inner ear, blood clotting, swimming of creatures large and small, and the flight of insects. Non-biological applications include sails, parachutes, flows of suspensions, and two-fluid or multifluid problems. Topics to be covered include: mathematical formulation of fluid-structure interaction in Eulerian and Lagrangian variables, with interaction equations involving the Dirac delta function; discretization of the structure, fluid, and interaction equations, including energy-based discretization of the structure equations, finite-difference discretization of the fluid equations, and IB delta functions with specified mathematical properties; a simple but effective method for adding mass to an immersed boundary; numerical simulation of rigid immersed structures or immersed structures with rigid parts; IB methods for immersed filaments with bend and twist; and a stochastic IB method for thermally fluctuating hydrodynamics within biological cells. Some recent developments to be discussed include stability analysis of the IB method and a Fourier-Spectral IB method with improved boundary resolution.

Course requirements include homework assignments and a computing project, but no exam. Students may collaborate on the homework and on the computing project, and are encouraged to present the results of their computing projects to the class.

Prerequisite: Familiarity with numerical methods and fluid dynamics.

(MATH-GA.2012 / CSCI-GA.2945) : High Performance Computing

Not offered AY 23/24

This class will be an introduction to the fundamentals of parallel scientific computing. We will establish a basic understanding of modern computer architectures (CPUs and accelerators, memory hierarchies, interconnects) and of parallel approaches to programming these machines (distributed vs. shared memory parallelism: MPI, OpenMP, OpenCL/CUDA). Issues such as load balancing, communication, and synchronization will be covered and illustrated in the context of parallel numerical algorithms. Since a prerequisite for good parallel performance is good serial performance, this aspect will also be addressed. Along the way you will be exposed to important tools for high performance computing such as debuggers, schedulers, visualization, and version control systems. This will be a hands-on class, with several parallel (and serial) computing assignments, in which you will explore material by yourself and try things out. There will be a larger final project at the end. You will learn some Unix in this course, if you don't know it already.

Prerequisites for the course are (serial) programming experience with C/C++ (I will use C in class) or Fortran, and some familiarity with numerical methods.

(MATH-GA.2011) Monte Carlo Methods

Fall 2023, Jonathan Weare and Jonathan Goodman

Topics : The theory and practice of Monte Carlo methods. Random number generators and direct sampling methods, visualization and error bars. Variance reduction methods, including multi-level methods and importance sampling. Markov chain Monte Carlo (MCMC), detailed balance, non-degeneracy and convergence theorems. Advanced MCMC, including Langevin and MALA, Hamiltonian, and affine invariant ensemble samplers. Theory and estimation of auto-correlation functions for MCMC error bars. Rare event methods including nested sampling, milestoning, and transition path sampling. Multi-step methods for integration including Wang Landau and related thermodynamic integration methods. Application to sampling problems in physical chemistry and statistical physics and to Bayesian statistics.

Required prerequisites:

A good probability course at the level of Theory of Probability (undergrad) or Fundamentals of Probability (masters)
Linear algebra: Factorizations (especially Cholesky), subspaces, solvability conditions, symmetric and non-symmetric eigenvalue problem and applications
Working knowledge of a programming language such as Python, Matlab, C++, Fortran, etc.
Familiarity with numerical computing at the level of Scientific Computing (masters)

Desirable/suggested prerequisites:

Numerical methods for ODE
Applied Stochastic Analysis
Familiarity with an application area, either basic statistical mechanics (Gibbs Boltzmann distribution), or Bayesian statistics

(MATH-GA.2012 / CSCI-GA.2945) Convex & Non Smooth Optimization

Spring 2024, Michael Overton

Convex optimization problems have many important properties, including a powerful duality theory and the property that any local minimum is also a global minimum. Nonsmooth optimization refers to minimization of functions that are not necessarily convex, usually locally Lipschitz, and typically not differentiable at their minimizers. Topics in convex optimization that will be covered include duality, CVX ("disciplined convex programming"), gradient and Newton methods, Nesterov's optimal gradient method, the alternating direction method of multipliers, the primal barrier method, primal-dual interior-point methods for linear and semidefinite programs. Topics in nonsmooth optimization that will be covered include subgradients and subdifferentials, Clarke regularity, and algorithms, including gradient sampling and BFGS, for nonsmooth, nonconvex optimization. Homework will be assigned, both mathematical and computational. Students may submit a final project on a pre-approved topic or take a written final exam.

Prerequisites: Undergraduate linear algebra and multivariable calculus

Q1: What is the difference between the Scientific Computing class and the Numerical Methods two-semester sequence?

The Scientific Computing class (MATH-GA.2043, fall) is a one-semester masters-level graduate class meant for graduate or advanced undergraduate students that wish to learn the basics of computational mathematics. This class requires a working knowledge of (abstract) linear algebra (at least at the masters level), some prior programming experience in Matlab, python+numpy, Julia, or a compiled programming language such as C++ or Fortran, and working knowledge of ODEs (e.g., an undergrad class in ODEs). It only briefly mentions numerical methods for PDEs at the very end, if time allows.

The Numerical Methods I (fall) and Numerical Methods II (spring) two-semester sequence is a Ph.D.-level advanced class on numerical methods, meant for PhD students in the field of applied math, masters students in the SciComp program , or other masters or advanced undergraduate students that have already taken at least one class in numerical analysis/methods. It is intended that these two courses be taken one after the other, not in isolation . While it is possible to take just Numerical Methods I, it is instead strongly recommended to take the Scientific Computing class (fall) instead. Numerical Methods II requires part I, and at least an undergraduate class in ODEs, and also in PDEs. Students without a background in PDEs should not take Numerical Methods II; for exceptions contact Aleks Donev with a detailed justification.

The advanced topics class on Computational Methods for PDEs follows on and requires having taken NumMeth II or an equivalent graduate-level course at another institution (contact Aleks Donev with a syllabus from that course for an evaluation), and can be thought of as Numerical Methods III.

Q2: How should I choose a first graduate course in numerical analysis/methods?

If you are an undergraduate student interested in applied math graduate classes, you should take the undergraduate Numerical Analysis course (MATH-UA.0252) first, or email the syllabus for the equivalent of a full-semester equivalent class taken elsewhere to Aleks Donev for an evaluation.
Take the Scientific Computing class (fall), or
Take both Numerical Methods I (fall) and II (spring), see Q1 for details. This is required of masters students in the SciComp program .

Ph.D. Program

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The range of possibilities for graduate study encompasses the areas of specialization of all of the faculty members in the field, who current number more than one hundred. The faculty members are drawn from fourteen departments in the College of Engineering, the College of Arts and Sciences, the College of Agriculture and Life Sciences and the Samuel Curtis Johnson Graduate School of Management. There is opportunity for further diversification on the choice of minor subjects.

Graduate students are admitted to the Field of Applied Mathematics from a variety of educational backgrounds that have a strong mathematics component. Generally, only students who wish to become candidates for the Doctor of Philosophy Degree are considered. About forty students are enrolled in the program, which usually requires four to five years to complete.

A normal course load for a beginning graduate student is three courses per term. Please see field requirements for details on courses. The Director of Graduate Studies in conjunction with the student's temporary committee chair will assist first-year students in determining the appropriate courses to meet individual needs. The program allows great flexibility in the selection of courses. Most students design their own course sequences, subject to requirements, to meet their own interests. Courses are typically chosen from the math department and many applications departments. The course requirements in detail can be found under Requirements .

Minor Subjects and Special Committee

Incoming students are assigned a temporary committee chair. Students are expected to select a permanent full committee by the end of the third semester. Students submit a "Special Committee Change and Selection Form" to the Graduate School to indicate their selection. Students may change committee members at any time by submitting a new form to the Graduate School. However, if they are post A-exam or three months within Ph.D. exam (B-exam), they must petition.

The Special Committee consists of a Chair/thesis advisor and at least one member for each of two minor subjects. One of the minor subjects must be mathematics. The other minor field can be from any area chosen by the student that is relevant to their doctoral research.

To be admitted formally to candidacy for the Ph.D. degree, the student must pass the oral admission to candidacy examination or A exam. This must be completed before the beginning of the student's fourth year. The admission to candidacy examination is given to determine if the student is "ready to begin work on a thesis." The content and methods of examination are agreed on by the student and his/her committee before the examination. The student must be prepared to answer questions on the proposed area of research, and to pass the exam, he/she must demonstrate expertise beyond just mastery of basic mathematics covered in the standard first-year graduate courses.

To receive an advanced degree a student must fulfill the residence requirements of the Graduate School. One unit of residence is granted for successful completion of one semester of full-time study, as judged by the chair of the Special Committee. The Ph.D. program requires a minimum of six residence units. This is not a difficult requirement to satisfy since the program generally takes four to five years to complete. A student who has done graduate work at another institution may petition to transfer residence credit but may not receive more than two such credits.

Thesis/B Exam

The candidate must write a thesis that represents creative work and contains original results in that area. The research is carried on independently by the candidate under the supervision of the chairperson of the Special Committee. When the thesis is completed, the student presents his/her results at the thesis defense or B exam.

Graduate Handbook

For further details on the program, see the Graduate Handbook .

Have question? Read our FAQ!

Applied Mathematics, PhD

Program description
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Computational, Computational Mathematics, Mathematical Models, Mathematical modeling, Mathematician, Mathematics, Mathematics Science, Performance, applied, approved for STEM-OPT extension, computing, dynamics, math, systems

Are you passionate about making a difference in the world of climate or environmental issues, or advancing the fight against cancer or infectious diseases? You can apply your enhanced mathematics expertise to devising solutions to these types of current problems.

This PhD program in applied mathematics is intended for students with superior computational and mathematical modeling ability. It emphasizes a solid mathematical foundation and promotes creative scholarship in an application discipline.

The School of Mathematical and Statistical Sciences has faculty in applied mathematics with outstanding transdisciplinary research programs that have strong external funding. Current research interests include mathematical epidemiology and mathematical ecology, mathematical neuroscience, environmental fluid dynamics and high-performance computing, imaging and inverse problems, supply chain dynamics, control and optimization, computational methods for ordinary and partial differential equations, analysis of differential equations, and geophysical and environmental fluid dynamics.

This program may be eligible for an Optional Practical Training extension for up to 24 months. This OPT work authorization period may help international students gain skills and experience in the U.S. Those interested in an OPT extension should review ASU degrees that qualify for the STEM-OPT extension at ASU's International Students and Scholars Center website.

The OPT extension only applies to students on an F-1 visa and does not apply to students completing a degree through ASU Online.

College/school: The College of Liberal Arts and Sciences
Location: Tempe
STEM-OPT extension eligible: Yes

84 credit hours, a written comprehensive exam, a prospectus and a dissertation

Required Core (3 credit hours) APM 505 Applied Linear Algebra (3)

Other Requirements (12 credit hours) APM 501 Differential Equations I (3) APM 502 Differential Equations II (3) APM 503 Applied Analysis (3) APM 504 Applied Probability and Stochastic Processes (3) APM 506 Computational Methods (3)

Electives and Research (57 credit hours)

Culminating Experience (12 credit hours) APM 799 Dissertation (12)

Additional Curriculum Information Students must pass:

two qualifying examinations
a written comprehensive examination
an oral dissertation prospectus defense

Students should see the department website for examination information.

Each student must write a dissertation and defend it orally in front of five dissertation committee members.

Electives are chosen from math or related area courses approved by the student's supervisory committee.

Students choose four out of the five courses listed for other requirements.

Applicants must fulfill the requirements of both the Graduate College and The College of Liberal Arts and Sciences.

Applicants are eligible to apply to the program if they have earned a bachelor's or master's degree in mathematics, applied mathematics, economics, engineering or a natural science from a regionally accredited institution.

Applicants must have a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in the last 60 hours of their first bachelor's degree program or a minimum cumulative GPA of 3.00 (scale is 4.00 = "A") in an applicable master's degree program

All applicants must submit:

graduate admission application and application fee
official transcripts
statement of education and career goals
three letters of recommendation
proof of English proficiency

Additional Application Information An applicant whose native language is not English must provide proof of English proficiency regardless of their current residency.

To demonstrate their competitiveness in an applicant pool, applicants must show evidence of coursework in linear algebra (equivalent to ASU course MAT 342 or MAT 343) and advanced calculus (equivalent to ASU course MAT 371). It is desirable that applicants have scientific programming skills.

Session	Modality	Deadline	Type
Session A/C	In Person	07/01	Final
Session A/C	In Person	12/10	Priority

Program learning outcomes identify what a student will learn or be able to do upon completion of their program. This program has the following program outcomes:

Apply concepts and skills from applied mathematics to conduct original research.
Able to complete original research in applied mathematics.
Apply advanced computational methods in their coursework and research.

Foundational knowledge in mathematics is required for building careers in science and technology. It can be applied in many different types of professions in fields that include engineering, life sciences, business, and economic and social sciences. These are just a few of the top careers possible with a doctorate in applied mathematics:

biostatistician
data scientist
financial analyst
government and military researcher
industrial researcher
mathematical modeling expert
mathematician
medical researcher
operations research analyst
university instructor and faculty member

School of Mathematical and Statistical Sciences | WXLR A213 [email protected] 480-965-3951

Committee on Computational and Applied Mathematics

Phd program, academic progress and milestones.

Course Requirements

First-year students are required to register for three courses per quarter for a total of nine (9) graduate courses during their first year in the program. They are required to follow the analytical sequence:

Applied Dynamical Systems ( CAAM 31410 ),

Applied Functional Analysis ( CAAM 31440 ),

Partial Differential Equations ( CAAM 31220 ),

as well as the computational sequence:

Mathematical Computation I: Matrix Computation ( CAAM 30900 ),

Mathematical Computation II: Optimization ( CAAM 31020 or CAAM 31015 ),

Applied Approximation Theory ( CAAM 31050 ).

They should receive a grade of B or above in each course and have an average of B+ or above in each sequence. The remaining three courses may be chosen freely from CAM-related graduate programs at The University of Chicago. Approval for the three electives is required from the first-year PhD student advisor.

Graduate students are required to complete a third sequence during their first three years in the program. The sequence is composed of

Machine Learning ( CAAM 37710 )

or equivalent and two classes from the following list:

Measure Theoretic Probability (STAT 381, STAT 383, STAT 385),

Data Assimilation and Inverse Problems,

Variational Methods in Image Processing,

Monte Carlo Simulations,

Numerical PDE,

Fast Algorithms,

Algorithms for Massive Datasets,

Computational Neuroscience (CAAM 42610),

Stochastic processes in gene regulation (CAAM 35420).

Students who do not complete these requirements as noted above may be placed on academic probation.

Graduate students need to complete at least twelve (12) CAM-related graduate courses to graduate.

Qualifying Exams

Graduate students take written qualifying exams at the end of their first year, typically in the month of June. They need to take two out of three exams from the analytical sequence and two out of three exams from the computational sequence.

Students failing all four exams may be dismissed from the program at the end of their first year.

Students failing between one and three exams will need to retake those same exams the following year unless CCAM provides an alternative path. Students failing any exam for a second time may be dismissed from the program at the end of their second year.

Thesis Advisor and Thesis Committee

Students are encouraged to identify a potential PhD advisor at the end of their first year to engage/enroll in a summer Reading & Research course. If such an advisor cannot be identified, students are required to present a plan for their first-year summer quarter that needs approval from CCAM.

PhD students are free to change PhD advisors during their enrollment in the program. PhD advisors are free to discontinue working with a PhD student and then cease to be the student’s advisor should the collaboration not meet expectations.

Students are required to form a thesis committee once they have a designated advisor and no later than the Spring quarter of their third year. The committee will first meet (in person) at the end of the student’s second year. If such a thesis committee cannot be formed at that time, students need to present a plan for their future in the program that needs approval from CCAM.

The thesis committee is composed of a minimum of three researchers physically present in Chicago. At least two members need to be affiliated with CCAM. Thesis committees report to CCAM on the student progress at the end of every academic year.

Students are expected to present progress in their PhD work to the thesis committee once during year 3, and again once during year 4. One of these meetings may be used for advancement to candidacy (see below).

Our expectation is for students to graduate at the end of their fifth year in the program. Staying in the program for a sixth year requires approval by CCAM. Students would need to petition by the end of Winter quarter of their fifth year, provide a research plan for completing their degree in a timely manner, and receive approval from their PhD advisor.

Proposal Presentation and Admission to Candidacy

No later than the end of Spring Quarter of the fourth year, students should have scheduled and completed a proposal presentation to their committee, in order to be advanced to candidacy. The proposal presentation is typically an hourlong meeting that begins with a 30-minute presentation by the student, followed by a question and discussion period with the committee. The proposal meeting will be scheduled by the student and their committee and reported to the CAM student affairs administrator. Acceptance of the proposal by the Dissertation Committee is a formal requirement of CAM’s Ph.D. program; all committee members must sign the form approving the proposal. After a successful proposal presentation, the student will be formally admitted to candidacy for the Ph.D. degree. By University rules, the dissertation defense cannot occur earlier than 8 months after admission to candidacy, and the student should keep this in mind when scheduling both the proposal presentation and the defense.

Following advancement to candidacy, during each year that the student remains, the student is required to have a yearly meeting with the dissertation committee leading up to the final thesis defense.

Dissertation Defense

The Ph.D. degree will be awarded following a successful defense and the electronic submission of the final version of the dissertation to the University's Dissertation Office. In this process, a number of University and Department deadlines have to be obeyed. Listed in reverse order, the steps are:

a) Submission of Final Version of Dissertation: The deadline is set by the University and is generally on a Friday in the 6th or 7th week of the quarter when the degree will be awarded. See:

Information for Ph.D. Students: https://www.lib.uchicago.edu/research/scholar/phd/students/
Dissertation Deadlines: https://www.lib.uchicago.edu/research/scholar/phd/students/dissertation-deadlines/
Dissertation Templates (LaTeX and Lyx): https://wiki.uchicago.edu/display/DissertationTemplate/Home

for this deadline as well as guidelines for the formatting of dissertations. b) Dissertation Defense : The thesis defense will be an open seminar announced to the department. Following the regular question-and-answer session, the committee will remain, together with any interested faculty, and continue questioning the candidate. The decision on the thesis will then be reached in a closed meeting of the faculty present. The defense is to be scheduled at least two weeks before the University deadline indicated in point (a). A final draft of the dissertation must be made available to the entire faculty 8 days before the dissertation presentation. c) Committee Approval of Scheduled Defense: A draft of the dissertation should be distributed to the members of the dissertation committee no later than five weeks before the dissertation defense. At least four weeks before the defense, the student must file a departmental form in the Department office, signed by all members of the dissertation committee, indicating that the student can reasonably expect to defend the thesis within four weeks. These rules delineate the minimum level of involvement of the dissertation committee. We strongly recommend that students set up their committees early and that they interact regularly with the members of their committees once they are established. In particular, we strongly recommend that those students wishing to complete the degree before September schedule their defense before the Summer Quarter, else unanticipated committee requirements may lead to the degree being delayed to the Winter Quarter.

Students with questions may contact Jonathan Rodriguez (Student Affairs Administrator), Bahareh Lampert (Dean of Students in the Physical Sciences Division), or Amanda Young (Associate Director, Graduate Student Affairs) in UChicagoGRAD.

Applied Mathematics, PHD

On this page:, at a glance: program details.

Location: Tempe campus
Second Language Requirement: No

Program Description

Degree Awarded: PHD Applied Mathematics

Degree Requirements

Curriculum plan options.

84 credit hours, a written comprehensive exam, a prospectus and a dissertation

Required Core (3 credit hours) APM 505 Applied Linear Algebra (3)

Electives and Research (57 credit hours)

Culminating Experience (12 credit hours) APM 799 Dissertation (12)

Additional Curriculum Information Students must pass:

two qualifying examinations
a written comprehensive examination
an oral dissertation prospectus defense

Students should see the department website for examination information.

Each student must write a dissertation and defend it orally in front of five dissertation committee members.

Electives are chosen from math or related area courses approved by the student's supervisory committee.

Students choose four out of the five courses listed for other requirements.

Admission Requirements

Applicants must fulfill the requirements of both the Graduate College and The College of Liberal Arts and Sciences.

All applicants must submit:

graduate admission application and application fee
official transcripts
statement of education and career goals
three letters of recommendation
proof of English proficiency

Additional Application Information An applicant whose native language is not English must provide proof of English proficiency regardless of their current residency.

Next Steps to attend ASU

Learn about our programs, apply to a program, visit our campus, application deadlines, learning outcomes.

Able to complete original research in applied mathematics.
Apply concepts and skills from applied mathematics to conduct original research.
Apply advanced computational methods in their coursework and research.

Career Opportunities

biostatistician
data scientist
financial analyst
government and military researcher
industrial researcher
mathematical modeling expert
mathematician
medical researcher
operations research analyst
university instructor and faculty member

Program Contact Information

If you have questions related to admission, please click here to request information and an admission specialist will reach out to you directly. For questions regarding faculty or courses, please use the contact information below.

[email protected]
480/965-3951

Graduate Programs

Applied mathematics.

The graduate program provides training and research activities in a broad spectrum of applied mathematics. The breadth is one of the great strengths of the program and is further reflected in the courses we offer.

The Division of Applied Mathematics is devoted to research, education and scholarship. Our faculty engages in research in a range of areas from applied and algorithmic problems to the study of fundamental mathematical questions. By its nature, our work is and always has been inter– and multidisciplinary. Among the research areas represented in the division are dynamical systems and partial differential equations, control theory, probability and stochastic processes, numerical analysis and scientific computing, fluid mechanics, computational biology, statistics, and pattern theory. Our graduate program in applied mathematics includes around 50 Ph.D. students, with many of them working on interdisciplinary projects. Joint research projects exist with faculty in various biology and life sciences departments and the departments of Chemistry, Computer Science, Cognitive and Linguistic Sciences, Earth, Environmental, and Planetary Sciences, Engineering, Mathematics, Physics and Neuroscience, as well as with faculty in the Warren Alpert Medical School of Brown University.

Application Information

Application requirements, gre subject:.

Not Required

GRE General:

Dates/deadlines, application deadline, completion requirements.

Eight courses, of which at least six must be at the 2000 level, at least six must be applied mathematics courses, and at least six must be completed with a grade of B or better; preliminary oral examination; two semesters of teaching; dissertation and oral defense.

Alumni Careers

Contact and Location

Division of applied mathematics, mailing address.

Program Faculty
Program Handbook
Graduate School Handbook

Overview of the PhD Program

For specific information on the Applied Mathematics PhD program, see the navigation links to the right.

What follows on this page is an overview of all Ph.D. programs at the School; additional information and guidance can be found on the Graduate Policies pages.

General Ph.D. Requirements

10 semester-long graduate courses, including at least 8 disciplinary. At least 5 of the 10 should be graduate-level SEAS "technical" courses (or FAS graduate-level technical courses taught by SEAS faculty), not including seminar/reading/project courses. Undergraduate-level courses cannot be used. For details on course requirements, see the school's overall PhD course requirements and the individual program pages linked therein.
Program Plan (i.e., the set of courses to be used towards the degree) approval by the Committee on Higher Degrees (CHD).
Minimum full-time academic residency of two years .
Serve as a Teaching Fellow (TF) in one semester of the second year.
Oral Qualifying Examination Preparation in the major field is evaluated in an oral examination by a qualifying committee. The examination has the dual purpose of verifying the adequacy of the student's preparation for undertaking research in a chosen field and of assessing the student's ability to synthesize knowledge already acquired. For details on arranging your Qualifying Exam, see the exam policies and the individual program pages linked therein.
Committee Meetings : PhD students' research committees meet according to the guidelines in each area's "Committee Meetings" listing. For details see the "G3+ Committee Meetings" section of the Policies of the CHD and the individual program pages linked therein.
Final Oral Examination (Defense) This public examination devoted to the field of the dissertation is conducted by the student's research committee. It includes, but is not restricted to, a defense of the dissertation itself. For details of arranging your final oral exam see the Ph.D. Timeline page.
Dissertation Upon successful completion of the qualifying examination, a committee chaired by the research supervisor is constituted to oversee the dissertation research. The dissertation must, in the judgment of the research committee, meet the standards of significant and original research.

Optional additions to the Ph.D. program

Harvard PhD students may choose to pursue these additional aspects:

a Secondary Field (which is similar to a "minor" subject area). SEAS offers PhD Secondary Field programs in Data Science and in Computational Science and Engineering . GSAS lists secondary fields offered by other programs.
a Master of Science (S.M.) degree conferred en route to the Ph.D in one of several of SEAS's subject areas. For details see here .
a Teaching Certificate awarded by the Derek Bok Center for Teaching and Learning .

SEAS PhD students may apply to participate in the Health Sciences and Technology graduate program with Harvard Medical School and MIT. Please check with the HST program for details on eligibility (e.g., only students in their G1 year may apply) and the application process.

In Applied Mathematics

First-Year Exploration
Areas of Application
AM & Economics
How to Declare
Who are my Advisors?
Secondary Field
Senior Thesis
Research for Course Credit (AM 91R & AM 99R)
AB/SM Information
Peer Concentration Advisors (PCA) Program
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How to Apply
PhD Timeline
PhD Model Program (Course Guidelines)
Oral Qualifying Examination
Committee Meetings
Committee on Higher Degrees
Research Interest Comparison
Collaborations
Cross-Harvard Engagement
Clubs & Organizations
Centers & Initiatives
Alumni Stories

Applied Mathematics

Undergraduate Program

The Applied Mathematics concentration consists of a broad undergraduate education in the mathematical sciences, especially in those subjects that have proved vital to an understanding of problems arising in other disciplines, and in some specific area where mathematical methods have been substantively applied. For concentrators, a core learning objective is building and demonstrating foundational knowledge in computation, probability, discrete, and continuous mathematics through the successful completion of the foundation and breadth courses. Students are also eligible to apply for an A.B./S.M. degree program.

Harvard School of Engineering offers a Doctor of Philosophy (Ph.D.) degree in Applied Mathematics. Doctoral students may earn the masters degree en route to the Ph.D. Students are drawn to Applied Mathematics by the flexibility it offers in learning about how to apply mathematical ideas to problems drawn from different fields, while remaining anchored to empirical data that drive these questions. Research and educational activities have particularly close links to Harvard’s efforts in Mathematics, Economics, Computer Science, and Statistics. Graduates go on to a range of careers in industry, academics, to professional schools in business, law, medicine, among others. All Ph.D.s are awarded through the Harvard Graduate School of Arts and Sciences.

PhD Program

More information and a full list of requirements for the PhD program in Mathematics can be found in the University Bulletin .

During their first year in the program, students typically engage in coursework and seminars which prepare them for the Qualifying Examinations . Currently, these two exams test the student’s breadth of knowledge in algebra and real analysis.

Starting in Autumn 2023, students will choose 2 out of 4 qualifying exam topics:

real analysis
geometry and topology
applied mathematics

Course Requirements for students starting prior to Autumn 2023

To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297.

Within the 27 units, students must satisfactorily complete a course sequence. This can be fulfilled in one of the following ways:

Math 215A, B, & C: Algebraic Topology, Differential Topology, and Differential Geometry
Math 216A, B, & C: Introduction to Algebraic Geometry
Math 230A, B, & C: Theory of Probability
3 quarter course sequence in a single subject approved in advance by the Director of Graduate Studies.

Course Requirements for students starting in Autumn 2023 and later

To qualify for candidacy, the student must have successfully completed 27 units of Math graduate courses numbered between 200 and 297. The course sequence requirement is discontinued for students starting in Autumn 2023 and later.

By the end of Spring Quarter of their second year in the program, students must have a dissertation advisor and apply for Candidacy.

During their third year, students will take their Area Examination , which must be completed by the end of Winter Quarter. This exam assesses the student’s breadth of knowledge in their particular area of research. The Area Examination is also used as an opportunity for the student to present their committee with a summary of research conducted to date as well as a detailed plan for the remaining research.

Years 4&5

Typically during the latter part of the fourth or early part of the fifth year of study, students are expected to finish their dissertation research. At this time, students defend their dissertation as they sit for their University Oral Examination. Following the dissertation defense, students take a short time to make final revisions to their actual papers and submit the dissertation to their reading committee for final approval.

Throughout the PhD Program

All students continue through each year of the program serving some form of Assistantship: Course, Teaching or Research, unless they have funding from outside the department.

Our graduate students are very active as both leaders and participants in seminars and colloquia in their chosen areas of interest.

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Applied Mathematics, Ph.D.

Download the Curriculum for Applied Mathematics, Ph.D.

Find out what courses you'll be taking

The Ph.D. in Applied Mathematics

Graduates with a master's in applied mathematics can expand their subject matter expertise by choosing a PhD in applied mathematics at Florida Tech. As one of only 30 applied mathematics programs in the United States, Florida Tech's doctoral program offers several specializations in the field, including nonlinear analysis, stochastic analysis, optimization, numerical analysis, scientific computing, and statistics.

A Degree with Real Flexibility

In addition to the areas of specialization, Florida Tech provides additional flexibility in its PhD in applied mathematics program, allowing doctoral students to design a curriculum that fits their specific research interests and career goals. As a national research university, Florida Tech is committed to providing students with a variety of applied mathematics research experiences, opening up careers in a wide range of industries.

Small Classes–World Renowned Faculty

Students in the PhD in applied mathematics program at Florida Tech work closely with professors and fellow students. A small faculty-to-student ratio creates a close-knit academic community that is often impossible at larger universities. Professors in the math department have doctoral degrees in applied and computational mathematics and statistics. Professors—not graduate students—teach all courses, supervise student research projects, and conduct their own meaningful research studies that are often open for student collaboration.

Advanced Research Opportunities

As in any doctoral program, research is the core of the academic program. The PhD in applied mathematics program explores many applied mathematics topics. Research is conducted in areas of science, engineering, medicine, and business through interdisciplinary teams, as well as in the areas of concentration needed for the doctoral degree program. Students take part in research projects such as dynamical systems and chaos theory, stem cell research, computational number theory, optimal control and inverse problems, and antagonistic stochastic games, to name a few.

Full-pay tuition scholarships are available for full-time doctoral graduate research assistants.

High-Tech Laboratory Facilities

The facilities and resources available for doctoral students at Florida Tech include access to the engineering and science labs, four mathematics labs that feature advanced software such as Wolfram Mathematica, MATLAB, the R Project, Sage, and IBM SPSS. Additionally, the new computational mathematics and statistics research lab includes a 55-inch touchscreen Mondopad.

Great Location

Many doctoral students in the PhD in applied mathematics program are working professionals living in close proximity to the campus in Melbourne, Florida. The university is also a top pick among students around the world for its location within the Florida High Tech Corridor–home to more than 5,000 high-tech companies and the fifth largest high-tech workforce in the nation.

Graduates with a PhD in applied mathematics work in a variety of fields ranging from engineering and science to medicine and economics. Some examples of the organizations, corporations, and research institutes that hire mathematicians include government labs, electronics and computer manufacturers, medical device companies, and financial services firms.

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Applied Mathematics - Doctor of Philosophy (PhD)

Mathematics 3 (M3) Building on Waterloo's Campus

Conduct mathematics-based research and generate new knowledge in a multidisciplinary environment with the PhD in Applied Mathematics program.

At North America’s only dedicated Faculty of Mathematics and the #1 school in Canada for mathematics and computer science, you’ll connect theoretical advances and innovative mathematics to develop novel solutions to the pressing problems facing today’s world.

Through a combination of coursework and original research, you’ll learn cutting-edge applications of mathematical theory in a broad range of fundamental and applied sciences, with five areas of research to choose from including control theory and dynamical systems, fluid mechanics, mathematical medicine and biology, mathematical physics, and scientific computation.

With the competitive edge provided by mentorship through the Faculty’s connections around the world, you’ll be prepar ed to pursue a career in academia, government or industry.

Research areas and degree options:

Control and Dynamical Systems
Fluid Mechanics
Mathematical Medicine and Biology
Mathematical Physics
Scientific Computing

Program overview

Department/School : Applied Mathematics Faculty : Faculty of Mathematics Admit term(s) : Fall (September - December), Winter (January - April), Spring (May - August) Delivery mode : On-campus Program type : Doctoral, Research Length of program : 48 months (full-time) Registration option(s) : Full-time, Part-time Study option(s) : Thesis

Application Deadlines

January 15 (for admission in September)
June 1 (for admission in January of the following year)
October 1 (for admission in May of the following year)

Key contacts

[email protected]

$Maliha Ahmed$

I see all these great scholars around me, like my supervisor Sue Ann Campbell. And like Anita Layton, Ghazal Geshnizjani, my committee members, and so many others in the department. I see their passion for what they do and their dedication to helping us grad students succeed. It’s very heartening. It motivates me to reach that level where I can give back in the same way. Maliha Ahmed, Applied Mathematics, PhD

Supervisors

Review the finding a supervisor resources

Admission requirements

Minimum grade point average: 78% or its equivalent
It is absolutely essential that the application for admission into the program contain evidence of potential for performing original research. This should be provided by successful completion of a Master's thesis in a mathematics-related discipline.
In some circumstances a student enrolled in the MMath program (thesis) in Applied Mathematics may transfer to the PhD program without completing their MMath program

Degree requirements

Review the degree requirements in the Graduate Studies Academic Calendar, including the courses that you can anticipate taking as part of completing the degree
Check out Waterloo's institutional thesis repository - UWspace to see recent submissions from the department of Applied Mathematics graduate students

Application materials

The SIF contains questions specific to your program, typically about why you want to enrol and your experience in that field. Review the application documents web page for more information about this requirement
If a statement or letter is required by your program, review the writing your personal statement resources for helpful tips and tricks on completion
Transcript(s)
Three references , normally from academic sources
TOEFL 90 (writing 25, speaking 25), IELTS 7.0 (writing 6.5, speaking 6.5)

Tuition and fees

Visit the graduate program tuition page on the Finance website to determine the tuition and incidental fees per term for your program

Review living costs and housing

Review the funding graduate school resources for graduate students

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Ph.D. in Applied Mathematics

See the catalog copy of the description of the Ph.D. in Applied Mathematics program.

1. Overview

A student in the Ph.D. in Applied Mathematics degree program must maintain satisfactory academic progress towards completion of the degree. Student satisfactory academic progress is primarily assessed by: (a) satisfactory coursework performance, (b) the Qualifying Examination, (c) the Dissertation Topic Approval Defense, and (d) the Dissertation Defense. Courses and the Qualifying Examination are used to ensure that the student has the breadth as well as the depth of knowledge needed for research success. The Dissertation Topic Approval Defense is used to ensure that the scope of dissertation research is important, that the plan is well thought out, and that the student has sufficient skills and thoughtfulness needed for success. The Dissertation Defense is used to assess the outcomes of the dissertation research, and whether or not the plan agreed upon by the Dissertation Committee has been appropriately followed.

The key requirements and milestones for the Ph.D. in Applied Mathematics degree are provided below. Failure to satisfy the requirements can result in suspension or dismissal from the program.

Minimum Hours
Interdisciplinary Minor
Core Courses
Additional “Core” Courses
Qualifying Examination
Dissertation Committee
Dissertation Topic Approval Defense
Dissertation Defense

2. Minimum Hours

To earn a Ph.D. in Applied Mathematics degree, a student must complete at least 56 approved post baccalaureate credit hours. This includes 2 hours of Responsible Conduct of Research (GRAD 8302), at least 18 hours of dissertation research and reading (MATH 8994), and the hours for the interdisciplinary minor. Graduation requirements mandate that students must achieve a minimum grade point average of 3.0 to graduate. Receiving more than two grades of C or a single grade of U in any graduate course will result in a suspension from the program.

A limited amount of transfer credit is allowed. In accordance with rules of the UNC Charlotte Graduate School, students are allowed to transfer up to 30 semester hours of graduate credit earned at UNC Charlotte or other recognized graduate programs. Only courses with grades A or B may be accepted for transfer credit. To receive transfer credit, students must file an online request (and submit all necessary documents including copies of transcripts and course syllabi if requesting to transfer non-UNC Charlotte courses).

File an online request to transfer post-Baccalaureate credits at http://gpetition.uncc.edu .

3. Interdisciplinary Minor

The interdisciplinary minor may be satisfied by 9 hours of graduate work outside the mathematics department, by 6 credit hours for a directed project in an area of application (MATH 8691/8692), or by a combination of external coursework and a directed project in an area of application totaling 9 credit hours.

It is expected that interdisciplinary minor courses shall in general be in STEM disciplines, but if there are applications in the student’s dissertation work towards the social sciences, courses in those fields are allowed too. The following is a non-exhaustive list of interdisciplinary minor courses allowed for several fields.

Physics: PHYS 5222, 5232, 5242, 5271, 6101 through 6201, 6203 through 6211, 6221 through 6271. A common example is PHYS 6210, but 5242 and 5271 would also be along the same lines.

Optics: OPTI 8101, 8102, 8104, 8105, 8211 with 8102, 8104, and 8211 being particularly relevant.

Molecular Biophysics: PHYS 6108/OPTI 8000, PHYS 6204, PHYS 6610 ( https://mbp.charlotte.edu/ )

Mechanical Engineering: MEGR 6116, 7113, 7164 for students who have specialized in math of fluids, while 6141, 6125, 7102, 7142, and 7143 for those specializing in continuum mechanics and elasticity.

Computer Science: ITCS 6111, 6114, 6150, 6153, 6155, 6165, 6170, 6171, 6220, 6226 with 6114 commonly taken.

Finance and Economics: Any of FINN or ECON courses listed under the MS Mathematical Finance program. Common examples include FINN 6203, 6210, 6211, and ECON 6206, 6113, 6219.

Mathematics Education: Any graduate level MAED courses such as MAED 6122, 6123, 6124.

4. Core Courses

All students in the Ph.D. in Applied Mathematics degree program must take the following courses, regardless of their intended area of study:

GRAD 8302 Responsible Conduct of Research (2 hours, usually required to take within the first year in the program)
MATH 8143 Real Analysis I (3 hours)
MATH 8144 Real Analysis II (3 hours)
MATH 8994 Doctoral Research and Reading (at least 18 hours)

Students whose intended area of study is statistics or mathematical finance are also required to take

MATH 8120 Theory of Probability I (3 hours)

5. Additional “Core” Courses

The following courses, though not explicitly required, are strongly recommended for each area of study.

Statistics: STAT 5123, 5124, 5126, 5127, 6115, 8127, 8133, 8135, 8137, 8139, 8122, 8123, 8027 (at least once)

Computational Math: MATH 5165, 5171, 5172, 5173, 5174, 5176, 8172, 8176

PDE and Mathematical Physics: MATH 5173, 5174, 8172

Probability: MATH 5128, 5129, 8120, 8125

Dynamical Systems: MATH 5173, 5174, 7275, 7276, 7277

Topology: MATH 5181, 8171, 8172 and independent study

Algebra: MATH 5163, 5164, 8163, 8164, and 8065 and/or independent study

Mathematical Finance: MATH 6202, 6203, 6204, 6205, 6206

6. Qualifying Examination

After being admitted to the Ph.D. program, a student is expected to take the qualifying examination within three semesters. This time limit may be extended up to two additional semesters in certain cases, depending on the background of the student and with program approval. The qualifying examination consists of two parts: the first part is a written examination based on Real Analysis I and II (MATH 8143/8144) or Theory of Probability I and Real Analysis I (MATH 8120/8143), the latter intended for a student with intended area of study in statistics or mathematical finance . The second part is a written examination based on two other courses chosen by the student to be specifically related to the student’s intended area of study and approved by the Graduate Coordinator. Typical choices for Part II are STAT 5126/5127, MATH 5173/5174, MATH 5172/5176, MATH 5163/5164, MATH 6205/6206, etc. The student may be allowed to retake a portion of the qualifying examination a second time if the student does not pass that portion on the first attempt within the guidelines of the Graduate School regulations pertaining to the qualifying examination and as overseen by the department Graduate Committee. A student who does not complete the qualifying examination as per the regulations of the Graduate School will be terminated from the Ph.D. program.

Complete and submit the following form after taking the Qualifying Examination. (Qualifying Exam Report Form) -> Graduate School form.

7. Dissertation Committee

After passing the Qualifying Examination, the student must set up a Dissertation Committee of at least four graduate faculty members, which must include at least three graduate faculty members from the Department of Mathematics and Statistics and one member appointed by the Graduate School. The committee is chaired by the student’s dissertation advisor. If the dissertation advisor is a graduate faculty member from an outside department or institution, a graduate faculty member from the Department of Mathematics and Statistics must be a co-chair of the committee. The Dissertation Committee must be approved by the Graduate Coordinator. After identifying and obtaining the signatures of the Dissertation Committee faculty, the Appointment of Doctoral Dissertation Committee Form must be sent to the Graduate School for the appointment of the Graduate Faculty Representative.

The Dissertation Committee should be appointed as soon as it is feasible, usually within a year after passing the Qualifying Examination.

Complete and submit the following form within a year of passing the Qualifying Examination. (Appointment of Doctoral Dissertation Committee Form) -> Graduate School form.

8. Dissertation Topic Approval Defense

Each student must present and orally defend a Ph.D. dissertation proposal after passing the Qualifying Examination and within ten semesters of entering the Program. The Dissertation Topic Approval Defense will be conducted by the student’s Dissertation Committee, and will be open to faculty and students. The dissertation proposal must address a significant, original and substantive piece of research. The proposal must include sufficient preliminary data and a timeline such that the Dissertation Committee can assess its feasibility.

The student should provide copies of the written dissertation proposal to the Dissertation Committee at least two weeks prior to the oral defense. At the discretion of the Dissertation Committee, the defense may include questions that cover the student’s program of study and background knowledge and techniques in the research area. The Dissertation Committee will unanimously grade the Dissertation Topic Approval Defense as pass/fail according to the corresponding rubrics. A student may retake the Dissertation Topic Approval Defense if he/she fails the first time. The second failed attempt will result in the termination of the student’s enrollment in the Ph.D. program. It is expected that the student first take the proposal defense by the ninth semester after enrollment to provide time for a second try should the first one fail. A doctoral student advances to Ph.D. candidacy after the dissertation proposal has been successfully defended. Candidacy must be achieved at least six months before the degree is conferred (so if you plan to graduate in a spring semester with the commencement on May 14, then you would need to successfully defend your dissertation topic by November 13 the prior year.)

The student must follow the following procedure in order to defend the dissertation proposal.

Communicate with the Dissertation Committee to set up a date/time for the oral defense, and reserve a defense room for at least two hours .
Send an electronic or written copy of the dissertation proposal to each member of the Dissertation Committee at least two weeks prior to the oral defense.
Inform the Graduate Coordinator the schedule at least one week prior to the oral defense.

Complete and submit the following form only after successfully passing the Dissertation Topic Approval Defense. (Petition for Topic Approval Form) -> Graduate School Form.

9. Dissertation

Each student must complete and defend a dissertation based on a research program approved by the student’s dissertation advisor which results in a high quality, original and substantial piece of research. The student must orally present and successfully defend the dissertation before the student’s doctoral dissertation committee in a defense that is open to the public. The Dissertation will be unanimously graded as pass/fail based on the corresponding rubrics by the Dissertation Committee and must be approved by the Dean of the Graduate School. Two attempts of the Dissertation Defense are permitted. The second failed attempt will result in the termination of the student’s enrollment in the Ph.D. program.

The student must follow the following procedure in order to defend the dissertation.

Communicate with the Dissertation Committee to set up a date/time for the public defense, and reserve a defense room for at least two hours with the help of the Graduate Coordinator.
Send an electronic or written copy of the dissertation to each member of the Dissertation Committee at least three weeks prior to the public defense.
Send an electronic copy of the dissertation in PDF as well as an abstract in a separate word file to the Graduate Coordinator at least two weeks prior to the public defense. The abstract is limited to 200 words, and does not have to be the same as the abstract included in the dissertation.
Prepare a presentation that should be at least 45 minutes long.

Complete and submit the following forms after defending your Dissertation. (Dissertation Report for Doctoral Candidates Form) -> Graduate School Form.

Also, submit the Dissertation Title Page with Original Committee Signatures.

In addition, submit ETD Signature Form with original committee and student signatures to the Graduate School within 24 hours after defense.

10. Graduation

Detailed information about graduation including the dissertation manual can be found on the Graduate School’s Graduation website . The Graduation process consists of the following steps and all three are required to complete the graduation process.

Complete the online graduation application – directions below – deadlines in the academic calendar.
Submit an approved candidacy application to the Graduate School – directions below – deadlines in the academic calendar.
Register for the term of graduation – deadlines in the academic calendar.

How to Apply for Graduation: Log into My UNCC. Select Banner Self Service, Student Services, Student Records and Online Graduation Application. Read the directions. Click “Continue” if this is the first time you have applied for graduation or “Create a New Application” if you have applied previously. After you complete all sections, remember to click the “Submit” button.

How to Access the Electronic Candidacy Application: Log into My UNCC. Select Banner Self Service, Student Services, Student Records and Apply for Candidacy for Graduate Students. Carefully read and follow all directions for each section. The total number of credit hours selected must be at least the minimum required for your degree or certificate. After you complete all sections, click the “Print” button. Do not change the page layout or formatting in any way. Take the printed document to your department for the Graduate Coordinator’s approval signature and then submit it to the Graduate School. Electronically submitted forms are not accepted.

Pay attention to the various deadlines in the official UNC Charlotte academic calendar , in particular, the following deadlines if you are planning to graduate.

Deadline for graduate students to file candidacy form
Deadline for graduate students to apply for graduation
Doctoral dissertation pre-defense formatting consultation deadline
Doctoral dissertation defense deadline
Doctoral dissertation post-defense formatting consultation deadline
Last day to submit doctoral dissertations to Graduate School

In addition, complete and submit the following forms to the graduate school.

Complete Survey of Earned Doctorates at https://sed.norc.org/doctorate . Print the Certificate of Completion and submit to the Graduate School within 24 hours after defense.
Contact Information Form
Copyright and Open Access Publishing Payment Form (optional)

Finally, a sample graduation checklist for doctotal graduates can be found here . Make sure

All courses with In Progress grades have been assigned grades; check with your advisor to ensure this happens. This must be completed 10 days prior to the commencement.
All courses in the current term have been assigned grades; check with your advisor or instructor to ensure this happens. This must be completed 10 days prior to the commencement.

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Applied and Computational Mathematics Master's Program Online

An online master's degree in applied and computational mathematics from Johns Hopkins University complements your knowledge with principles that can be applied to almost every discipline of science, engineering, industry, and technology—from defense technology and business to public policy and biomedicine.

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LIVE Lab at the Applied Physics Laboratory

Applied and Computational Math Program Overview

Johns Hopkins Engineering for Professionals online applied and computational mathematics master’s is one of the premier graduate degree options in our top-ranked online engineering master’s program and a leading computational mathematics master’s program in the industry. The advanced-level curriculum teaches students the key steps to incorporate design and mathematical algorithms into modern technologies.

Choose from highly relevant courses like Statistical Methods and Data Analysis, Real Analysis, and Matrix Theory to support your subject-matter interests. Whether you work to develop prototypes in manufacturing or create models to predict long-term climate change, the coursework emphasizes applied and theoretical aspects of the field, so you can:

Gain high demand skills to advance in industries that rely on mathematical modeling and computational science
Solve probability problems, including finding properties of distribution functions
Apply statistical software confidently
Interpret and solve simple regression models
Understand the distinction between axioms, definitions, and theorems
Learn on your terms and select a flexible course schedule in a format that works best for you

Master’s Degree Focus Areas

A focus area can be selected but is not required for the computational mathematics master’s .

Applied Analysis : Bring together mathematical topics such as differential equations, dynamical systems, approximation theory, number theory, topology, and Fourier analysis.
Information Technology and Computation : Apply a range of tools—such as neural networks, cryptography, and data mining—to solve business and organizational problems.
Operations Research : Employ techniques such as optimization and game theory across the employment spectrum in industries such as education, transportation, and public services.
Probability and Statistics : Measure randomness and how to collect, analyze, and interpret numerical data in such a way as to obtain useful information.
Simulation and Modeling : Learn to approximate a process or system over time with commonly used analytical tools like Monte Carlo Methods, Markov Chains, and queuing theory.

FOCUS AREA REQUIREMENTS

We offer three Applied and Computational Mathematics degree options; you can earn a Master of Science in Applied and Computational Mathematics, a Post-Master’s Certificate, or a Graduate Certificate.

Applied and Computational Mathematics Courses

Get details about course requirements, prerequisites, focus areas, and electives offered within the program. All courses are taught by subject-matter experts who are executing the technologies and techniques they teach. Selected undergraduate-level courses are also offered to provide mathematical background for the program. These 100- and 200-level courses are not for graduate credit. Some students may find one or more of these courses useful as a refresher or to fill gaps in their prior education.

Student Thesis and Research Papers/Projects

Learn about the requirements for completing research or a thesis in Applied and Computational Mathematics.

Self-assessment Math Placement Exams

Assessment examinations are available for Precalculus, Calculus 1, Calculus 2, and Calculus 3/Multivariable Calculus. Each assessment exam is an advisory tool to help you and your academic advisor gauge your preparedness for mathematics at a proper level here at EP. The exam is not a means to “pass out” of a particular course, and a waiver will not be granted solely based on an exam score.

Program Contacts

James spall.

Amanda Harwell

Andrew marshall, tuition and fees.

Did you know that 78 percent of our enrolled students’ tuition is covered by employer contribution programs? Find out more about the cost of tuition for prerequisite and program courses and the Dean’s Fellowship.

Why Hopkins?

Build on your applied and computational mathematics degree by engaging with all the rest Johns Hopkins has to offer.

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Expert Faculty - Study with faculty who are practicing scientists and notable professionals with corporations and government entities, including the Johns Hopkins Applied Physics Lab, NASA, Raytheon, and the U.S. Department of Defense. Exceptional one-on-one mentoring sets you on a course to be a confident, knowledgeable leader. Learn More

Beyond Rankings: We Help You Fulfill Your Vision - We are proud to be ranked among the top online graduate engineering schools by U.S. News & World Report . But we’re about more than just numbers and rankings—we’re focused on making sure you flourish as a learner and engineer. Learn More

Network and Connect - Your knowledge is stronger with a network. In the applied and computational mathematics program, you will make career-advancing connections with accomplished scientists and engineers who represent a variety of disciplines across many industries. Learn More

“ I enjoyed the flexibility of attending part-time, the personableness of the instructors in the program, and the content of the courses. ”

Applied and Computational Mathematics FAQs

I don't have an engineering background, can i still apply to this program.

Yes. If we are otherwise willing to accept the student, we will determine which prerequisites are still needed as part of the review process. You will then be admitted provisionally until those courses have been successfully completed.

What is the difference between computational mathematics vs computer science?

Generally speaking, computation mathematics refers to the mathematics that fuels a computer’s ability to solve complex equations, while computer science refers to the science that goes into building and innovating the computer itself. A computer science master’s program will focus more on the building and operations of computers while a computational mathematics master’s program leans more into the mathematics that computers use.

What can I do with an applied and computational mathematics degree?

Applied and computational mathematics jobs can range from genetic and healthcare research to software engineering and machine learning and over into statistics or actuarial science. You can also pursue careers in industries like medical research, international banking, and software development—just to name a few.

Academic Calendar

Find out when registration opens, classes start, transcript deadlines and more. Applications are accepted year-round, so you can apply any time.

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5 Careers in Applied Mathematics

Interested in pursuing an advanced career in applied mathematics? Learn which industries and occupations are available to you with JHU EP.

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Master of Science in Applied and Computational Mathematics - Online

Applied mathematics is an interdisciplinary field and one of the most dynamic areas of study in all of science. It has applications in physics, engineering, oceanography, atmospheric sciences, ecology, evolutionary biology, neuroscience, economics and a number of other disciplines.

In the online Master of Science in Applied & Computational Mathematics at the University of Washington, you’ll get an outstanding education and earn a highly marketable degree . Graduates of this top-ranked program leave with the knowledge and skills to become leaders in the field and help tackle some of the biggest challenges facing society today.

The online Master of Science in Applied & Computational Mathematics is offered by the Department of Applied Mathematics , which offers graduate degrees both on campus and online . A self-sustaining fee-based degree, it is administered in partnership with UW Continuum College .

Prospective students should have an undergraduate degree in mathematics, applied mathematics or another branch of science or engineering and have completed all prerequisite coursework. For complete admissions requirements, see the Admissions page. Because this rigorous program is offered completely online, students who are organized and highly motivated are most likely to be successful.

Please note: due to overlap between the online MS curriculum and our advanced undergraduate courses and the limited nature of online course offerings, applicants who have already taken one or more of AMATH 401, 402, 403 are ineligible for admission to the online program.

Minimum Admission Requirements

Bachelor's degree from a regionally accredited college or university in the United States or its equivalent from a foreign institution
A cumulative GPA of 3.2 or higher over the last 90 quarter hours (60 semester hours) of undergraduate work
Demonstrated English language proficiency for applicants whose native language is not English

Background and Prerequisites

Applicants should hold a bachelor's degree in mathematics, applied mathematics or another branch of science or engineering. You should also have completed coursework in:

Calculus series (advanced calculus and/or real analysis strongly recommended but not required)
Differential equations
Linear algebra
Numerical analysis or scientific computing * (you should have the ability to program in Matlab, C, C++, Python, Fortran or a similar scientific computing language)

For a full list of requirements by specific program, please see this guide . To earn the degree, you must complete a minimum of nine courses, including:

Four core courses (20 credits total)
One elective from applied math (at least 4 credits)
Minimum of 36 credits *
GPA of 2.7 or higher in each class and an overall GPA of 3.2 or higher

* On average, students complete the program with 42 credits.

Core Courses

You are required to take these four core courses:

AMATH 501: Vector Calculus & Complex Variables
AMATH 502: Introduction to Dynamical Systems & Chaos
AMATH 503: Methods for Partial Differential Equations
AMATH 581: Scientific Computing

In addition to electives in applied mathematics, you may be able to take online elective courses outside the department. These courses must be worth a minimum of three credits, graduate level, numerically graded and mathematically relevant. Check with your adviser before enrolling an elective course to make sure it will count toward your degree.

Satisfactory Performance and Progress

At all times, all Master’s students need to make satisfactory progress towards finishing their degree. Satisfactory progress in course work is based on grades. Students are expected to maintain a grade point average of 3.2 or higher. The Graduate School rules regarding satisfactory progress are detailed in Policy 3.7: Academic Performance and Progress . Typically, the Department of Applied Mathematics follows the recommendations of the Graduate School. We encourage all students to explore and utilize the many available resources across campus.

Below is a list of all applied mathematics courses offered in this program. You do not need to complete every course listed to earn your degree. Please keep in mind that some courses are not offered every year, as noted below.

Note: You are required to take four core courses: AMATH 501, 502, 503 and 581.

Autumn Quarter

AMATH 501: Vector Calculus & Complex Variables (5)
AMATH 581: Scientific Computing (5)
AMATH 584: Applied Linear Algebra & Introductory Numerical Analysis (5)

Winter Quarter

AMATH 502: Introduction to Dynamical Systems & Chaos (5)
AMATH 515: Fundamentals in Optimization (5) (offered odd years)
AMATH 582: Computational Methods for Data Analysis (5)
AMATH 585: Numerical Analysis of Boundary Value Problems (5) (offered even years)

Spring Quarter

AMATH 503: Methods for Partial Differential Equations (5)
AMATH 575: Dynamical Systems (5) (offered odd years)
AMATH 583: High-Performance Scientific Computing (5)
AMATH 586: Numerical Analysis of Time-Dependent Problems (5) (offered even years)

You can also complete four credits of independent research by taking AMATH 600 .

The UW online Master of Science in Applied & Computational Mathematics is well suited to working professionals and those who live outside the Seattle area. All classes, readings, assignments and discussions are accessed online, meaning you have the flexibility to study on your schedule and earn a UW degree from anywhere in the world that has high-speed internet service.

In many ways, online courses are similar to classroom courses. Along with the rest of your cohort, you start each course at the beginning of the quarter, follow a weekly schedule and meet regular deadlines. You need to keep up with all lectures, readings, activities and assignments as scheduled and complete all of your work by the quarter's end. Unlike on-campus students, you can choose when and where to do your coursework within this structure.

Course lectures are available in real time via live streaming and on demand starting two hours after the class ends. To access courses, you will need to connect your computer to a robust online learning management system called Canvas. This web-based software allows you to access lectures and other course materials, upload assignments and interact with your instructors and fellow students through discussion boards and other online features. Some faculty may use an alternative online classroom system.

Online students must arrange for an approved proctor to monitor their midterm(s) and final exam. Proctored exams for online students should be taken on the same day (Pacific Time) they’re administered to classroom students; any exceptions must be approved by the instructor. The proctor approval process is outlined in detail here .

Technology Requirements

Computer able to run a recent version of a major web browser such as Chrome, Edge, Firefox or Safari
Reliable high-speed internet connection
Student version of MATLAB (recommended)

The online Master of Science in Applied & Computational Mathematics is a self-sustaining, fee-based program administered by the UW Department of Applied Mathematics in collaboration with UW Continuum College .

Course fees are charged on a per-credit basis and are the same for Washington state resident students and nonresident students. In addition to these fees, students pay other required fees each quarter, including registration, U-PASS and technology fees. Payment is due by the third Friday of the quarter.

Cost per credit: $1,112 Minimum number of credits required: 36*

* Students complete an average of 42 credits to finish the degree.

This estimate is based on 2024–2025 rates and does not factor in textbooks, software or any annual fee increases.

Students in the program can apply for various forms of financial aid to help cover their educational costs, including federal financial aid , scholarships and loans. For more information, visit the fee-based programs page of the UW Student Financial Aid website. Students in fee-based programs are not eligible for tuition exemptions or University grants.

Graduate Student Funding

The Graduate School’s Office of Fellowships & Awards is a resource for students seeking information about fellowships, awards and assistantships. The Graduate Funding Information Service (GFIS) helps UW graduate students in their search for funding opportunities for graduate school-related expenses. GFIS representatives host workshops, post funding announcements and meet one-on-one with students.

Some employers will cover all or part of the cost of a professional education. Check with your employer to see if such a program is available.

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Major in Mathematics

First upper-division math courses.

It should be emphasized that the character of mathematics changes sharply between lower and upper-division courses. The role of computation diminishes and there is a greater emphasis on deductive reasoning. While some students find the theoretical approach more congenial, most find upper-division courses more difficult. Because of this, it is strongly recommended that only students who earned grades of B- or better in all of Math 53, Math 54 or Math 56, and Math 55 apply to the major programs in Mathematics or Applied Mathematics. Additionally, the advising staff recommend Mathematics 110 as your first upper-division class. Students are more successful in making the transition with this course. Math 104 is a particularly demanding class and should be taken later in your program. Be aware that top students spend 12 to 15 hours per class beyond the lectures and sections, so plan your course load accordingly.

Eligibility to Declare the Major

You are eligible to declare the major in Mathematics or Applied Mathematics if you have met ALL of the following criteria:

Completion of Math 1A & Math 1B (or equivalent) with averages grades of at least "C". For our policy on Advanced Placement scores, please see the following link .
Completion of Math 53, Math 54 or Math 56, and Math 55 (or equivalent) with minimum grades of "C" in each, or completion of two of those three courses (with minimum grades of "C" in each) and currently enrolled in the third. If declaring while currently enrolled in the final lower-division requirement, that course will need to be completed with a letter grade of at least "C". Please note that we will only accept Computer Science 70 in lieu of Math 55 if you are declared major in Computer Science or Electrical Engineering and Computer Science and declare Mathematics/Applied Mathematics as an additional major.
If you have already taken one or more upper division math courses, you should have a grade point average of at least 2.0 from those courses completed at the time of declaration. Note, however, that you do not need to have completed an upper division math course in order to declare.

Any alterations to the above requirements must be authorized (in writing) by the Head Major Advisor, upon referral from an Undergraduate Advisor in 964 or 965 Evans Hall.

Major Declaration Procedures

Submit an Application for the Major in Mathematics/Applied Mathematics to our dedicated declaration email address, both of which you can find our our declaration webpage .

Note that double majors require signatures from both your departments. If we are the first to sign your Double Major Petition, we will send it back to you to take to your second department. If your Double Major Petition is already signed by your first department, we can forward it to L&S Advising for final approval.)

Honors Program

See our Honors page for information about graduating with honors in Math or Applied Math.

Course Enrollment and CalCentral

Each semester advising holds are placed on math and applied math majors who have been declared for more than one semester. Mathematics and Applied Mathematics majors must consult with their Faculty Advisor for their first CalCentral registration period after declaring the major. In subsequent semesters, they may meet with the Staff Advisors. Meeting the Faculty or Staff Advisors should take place prior to the student's enrollment appointment to ensure removal of the hold in a timely manner. Before meeting with the Advisor, the student should plan a tentative program for the coming semester, and have an overall plan for completing the major. Enrollment packets consisting of a Course Approval Form (green) and a Major Checklist (white) which shows your completed courses and grades will be available in the Main Office (970 Evans) two weeks prior to the start of Phase I enrollment appointments. Faculty Advisors hold regular office hours during the academic year. These hours are also posted on the bulletin board outside 964 Evans. It is best to allow time for more than one meeting in case decisions depend on information not available at the first visit. When the Advisor and the student have agreed on a program of study, the Advisor will sign the Course Approval Form (green). Approved electives should be indicated on the bottom of the program form and initialed by the Advisor. Major holds are released by the Staff Advisors in 964 and 965 Evans Hall. Admitted transfer students should participate in orientation programs during the Summer preceding their first semester at Cal. Returning students should see their faculty advisor or the Undergraduate Advisor during the semester prior to their readmitted term. Although students are formally required to see their Faculty Advisors only when they first declare the major, they are strongly encouraged to consult with them, or seek the advice of any faculty member, at any time. If the Advisor's office hours conflict with the student's classes, the student should schedule an appointment with via email.

Credit by Examination

Outstanding lower-division students may choose to fulfill one or more of the lower-division requirements via credit-by-exam. Although the University awards only P/NP grades for credit-by-exam, credit-by-exam in any of the lower division prerequisite classes is acceptable for entry into the major. The Credit by Examination Petition is available through the following link on the Office of the Registrar's forms website. In order to file the petition, the student must acquire the approval of: (a) an instructor willing to administer the examination, and (b) the Major Advisor, ( only if already declared ). The list of eligibility criteria for Credit by Examination can be found on page two of the petition. (Note: you must be registered in the term in which the examination is to be taken; you may only take Credit by Exam in Fall and Spring terms; you must already have a 2.0 or better UC GPA - meaning it can be taken only after at least one term at UC.)

Course Equivalency

Equivalency of courses taken at other colleges and universities should be determined early in the application process. Articulation agreements with the California Community Colleges can be found on assist.org and non-California Community College coursework will be individually evaluated by a Non-Major Faculty Advisor prior to the student declaring the major or minor. For more information about this process, visit our Course Equivalency website .

Program Changes

Students can add or drop courses via CalCentral through the WEDNESDAY of the FOURTH week of classes. Grading option changes from letter grade to Pass/No Pass or from Pass/No Pass to letter grade can be done via CalCentral through the TENTH week of classes. Any student with fewer than 13 units needs permission from L&S Undergraduate Advising, located on the 2nd floor of Evans Hall, for a reduced study load.

Minimum and Maximum Limits of Number of Mathematics Courses Taken

Majors must take a minimum of four upper-division courses to establish residency in either of the math majors. The only limitation on the maximum number of upper-division and graduate mathematics courses a major may take is a College of Letters and Science regulation which states that students cannot register beyond the semester in which s/he surpasses their 130th unit. Advance planning can result in hitting 130 units and having an additional semester available, should you need it. An Undergraduate Advisor in 964 or 965 Evans can assist you.

Passed/Not Passed Grading (P/NP)

Courses taken to fulfill major requirements must be taken for a letter grade. The one exception is four units of Mathematics 199 (offered pass/not pass only) which may be used if approved by one's Faculty Advisor. Mathematics 199 cannot be used to study material covered in standard courses. To be eligible for enrollment, a student must have completed 60 units and have a minimum cumulative grade point average of 2.0. Additional regulations concerning 199 courses are outlined in the College of Letter and Science Earning Your Degree Guide. Staff in 970 Evans can assist students with the enrollment procedure.

Probation and Dismissal

A mathematics major whose cumulative grade-point average in the upper-division major taken at Berkeley falls below 2.0 will be placed on departmental probation. The departmental grade-point average computation includes both required courses in the major and approved electives. Any additional upper-division or graduate mathematics courses which are not used to satisfy major requirements are exempted. Students are expected to check their grades at the end of each semester. A student on probation will be subject to dismissal from the major if the grade-point average is not brought up to 2.0 within the following term. Questions concerning probation and dismissal may be directed to an Undergraduate Advisor in 964 or 965 Evans or the College of Letters and Science Advising, 206 Evans Hall.

Additional Academic Assistance

The Undergraduate Program Office, 970 Evans Hall, maintains a list of tutors for students seeking assistance. There are tutors listed for mathematics courses at all levels, from the most basic, precalculus courses, through upper-division, and even including basic graduate level courses. Students make arrangements with tutors on an individual basis. The Student Learning Center , located in the Cesar Chavez Center, offers group and drop-in tutoring for the basic lower division classes: Mathematics 1A-1B, and 53-54. Call (510) 642-7332 for scheduling and other information. There are also Academic Centers located at the dorms that provide drop-in tutoring during the evenings.

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Applied Mathematics Doctoral Program
The Applied Mathematics PhD Program has a very strong track record in research and training. Placement of PhD students has been outstanding, with recent PhD students taking tenure-track/tenured faculty jobs at institutions such as Carnegie Mellon, Columbia, Drexel, Purdue, Tsinghua, UC Santa Cruz, Utah, Washington and alike, as well as private sector jobs in leading financial and high-tech ...
Applied Mathematics (Ph.D.)
Illinois Tech's Ph.D. program in Applied Mathematics is a flagship graduate program that prepares talented mathematicians and statisticians for careers in research or academia through a rigorous education, which includes advanced coursework, independent study, and original research. With almost 100 percent job placement at graduation, our ...
PhD Program
Program Type. PhD. Mode of Study. On Campus. With an emphasis on mathematical reasoning, mathematical modeling and computation, interdisciplinary, and the development of new methodology, the department's doctoral program produces graduates with broad expertise, who have worked in cutting-edge advances in applied mathematics and statistics ...
Ph.D. Program
Course requirements for the Ph.D. program. Eight courses from the following nine: AMATH 561, 562, 563. AMATH 567, 568, 569. AMATH 584, 585, 586. AMATH 600: two, 2-credit readings, each with a different faculty member, to be completed prior to the start of the student's second year. Students must take a minimum of 15 numerically graded courses.
Applied Math
Courses in Applied Mathematics. The following list is for AY 2023/2024:-----(MATH-GA.2701) Methods Of Applied Math Fall 2023, Oliver Buhler. Description: This is a first-year course for all incoming PhD and Masters students interested in pursuing research in applied mathematics. It provides a concise and self-contained introduction to advanced ...
PhD in Applied Mathematics
PhD in Applied Mathematics Degree. Applied Mathematics at the Harvard John A. Paulson School of Engineering is an interdisciplinary field that focuses on the creation and imaginative use of mathematical concepts to pose and solve problems over the entire gamut of the physical and biomedical sciences and engineering, and increasingly, the social sciences and humanities.
Ph.D.
Financial support for Doctoral studies is limited to five years after admission to the Ph.D. program in the Department of Applied Mathematics. Support for an additional period may be granted upon approval of a petition, endorsed by the student's thesis supervisor, to the Graduate Program Coordinator. What research opportunities does your ...
Ph.D. Program
Graduate students are admitted to the Field of Applied Mathematics from a variety of educational backgrounds that have a strong mathematics component. Generally, only students who wish to become candidates for the Doctor of Philosophy Degree are considered. About forty students are enrolled in the program, which usually requires four to five ...
Applied Mathematics, PhD
Degree awarded: PHD Applied Mathematics. This PhD program in applied mathematics is intended for students with superior computational and mathematical modeling ability. It emphasizes a solid mathematical foundation and promotes creative scholarship in an application discipline. The School of Mathematical and Statistical Sciences has faculty in ...
PhD Program
Students are expected to present progress in their PhD work to the thesis committee once during year 3, and again once during year 4. One of these meetings may be used for advancement to candidacy (see below). Our expectation is for students to graduate at the end of their fifth year in the program. Staying in the program for a sixth year ...
Applied Mathematics, PHD
Applicants must fulfill the requirements of both the Graduate College and The College of Liberal Arts and Sciences. Applicants are eligible to apply to the program if they have earned a bachelor's or master's degree in mathematics, applied mathematics, economics, engineering or a natural science from a regionally accredited institution.
Applied Mathematics
Our graduate program in applied mathematics includes around 50 Ph.D. students, with many of them working on interdisciplinary projects. Joint research projects exist with faculty in various biology and life sciences departments and the departments of Chemistry, Computer Science, Cognitive and Linguistic Sciences, Earth, Environmental, and ...
PhD in Applied Mathematics
For specific information on the Applied Mathematics PhD program, see the navigation links to the right. What follows on this page is an overview of all Ph.D. programs at the School; additional information and guidance can be found on the Graduate Policies pages.
Applied Mathematics
Graduate. Harvard School of Engineering offers a Doctor of Philosophy (Ph.D.) degree in Applied Mathematics. Doctoral students may earn the masters degree en route to the Ph.D. Students are drawn to Applied Mathematics by the flexibility it offers in learning about how to apply mathematical ideas to problems drawn from different fields, while ...
PhD Program
PhD Program. More information and a full list of requirements for the PhD program in Mathematics can be found in the University Bulletin. During their first year in the program, students typically engage in coursework and seminars which prepare them for the Qualifying Examinations . Currently, these two exams test the student's breadth of ...
Applied Mathematics, Ph.D.
The PhD in applied mathematics program explores many applied mathematics topics. Research is conducted in areas of science, engineering, medicine, and business through interdisciplinary teams, as well as in the areas of concentration needed for the doctoral degree program. Students take part in research projects such as dynamical systems and ...
Ph.D. Program
In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements. During the first year of the Ph.D. program: Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics. Pass the six-hour written Preliminary Examination covering calculus ...
Applied Mathematics
Conduct mathematics-based research and generate new knowledge in a multidisciplinary environment with the PhD in Applied Mathematics program. At North America's only dedicated Faculty of Mathematics and the #1 school in Canada for mathematics and computer science, you'll connect theoretical advances and innovative mathematics to develop ...
Best Mathematics Online PhD programs
The quality of an online PhD in Mathematics is largely the same as a traditional on-campus PhD mathematics program, only that the online version can be completed entirely online. ... European Mathematical Society, and the International Council for Industrial and Applied Mathematics among many others. These are all credible bodies, demonstrating ...
Ph.D. in Applied Mathematics
To earn a Ph.D. in Applied Mathematics degree, a student must complete at least 56 approved post baccalaureate credit hours. This includes 2 hours of Responsible Conduct of Research (GRAD 8302), at least 18 hours of dissertation research and reading (MATH 8994), and the hours for the interdisciplinary minor. Graduation requirements mandate that ...
Applied Mathematics PhD
Requirements for the Mathematics and Applied Mathematics PhDs differ only in minor respects, and no distinction is made between the two in day-to-day matters. Graduate students typically take 5-6 years to complete the doctorate. Continuing students wishing to transfer from one program to another should consult the graduate advisor in 910 Evans ...
Graduate Studies in Mathematics
Math 6470: Analytic Methods of Applied Mathematics. Math 7010-7020: Topology I & II. Math7150: Probability Theory I. Math 7110-7120: Algebra I & II. Math 7210-7220: Analysis I & II. Math 7240: Mathematical Statistics. Math 7260: Linear Models. Math 7291-7292: Algebraic Geometry I & II. Math 7310-7320: Applied Math I & II. Math 7360: Data Analysis
MS in Applied & Computational Mathematics
Applied and Computational Math Program Overview. Johns Hopkins Engineering for Professionals online applied and computational mathematics master's is one of the premier graduate degree options in our top-ranked online engineering master's program and a leading computational mathematics master's program in the industry. The advanced-level curriculum teaches students the key steps to ...
Master of Science in Applied and Computational Mathematics
The online Master of Science in Applied & Computational Mathematics is offered by the Department of Applied Mathematics, which offers graduate degrees both on campus and online. A self-sustaining fee-based degree, it is administered in partnership with UW Continuum College. On this Page: Admissions; Degree Requirements; Course Sequence; Online ...
Are there any online PhD programs in Math? : r/gradadmissions
A doctorate is a research degree, which means you are intensely studying one thing at the boundaries of knowledge about the field. It isn't like a law degree or MBA in that regard. But keep researching and asking questions. A PhD is by definition a research based degree (about 80% research to 20% classes).
B.S. in Applied Mathematics : The University of Akron, Ohio
Program Highlights. UA has a reputation for excellence in applied sciences and engineering. The Department of Mathematics builds on this tradition and focuses on a modern and practical approach to mathematics, combining theory and application with an emphasis on applied interdisciplinary mathematics.
Major in Mathematics
Each semester advising holds are placed on math and applied math majors who have been declared for more than one semester. Mathematics and Applied Mathematics majors must consult with their Faculty Advisor for their first CalCentral registration period after declaring the major. In subsequent semesters, they may meet with the Staff Advisors.
Director of Interdisciplinary STEM Education in Raleigh, NC for ...
Candidates must possess a PhD in a STEM scientific field such as Chemistry, Biological Sciences, Biochemistry, Biology, Physics, Mathematics, Statistics, or Marine, Earth, and Atmospheric Sciences. Scientist with a record of accomplishment in research, teaching, supervision, and administration.
High Throughput Antibody Characterization Scientist in Livermore, CA
For more than 60 years, the Lawrence Livermore National Laboratory has applied science and technology to make the world a safer place.Livermore's defining responsibility is ensuring the safety, security and reliability of the nation's nuclear deterrent. Yet LLNL's mission is broader than stockpile stewardship, as dangers ranging from ...