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Applied Mathematics & Statistics
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Requirements for the M.S. Degree

The M.S. degree in the Department of Applied Mathematics and Statistics requires the satisfactory completion of a minimum of 30 graduate credits, excluding research, teaching and internship courses (AMS 599, 698, 699, 700, and 701). The average for all courses taken must be B or higher, and at least 18 credits of all courses taken must carry a grade of B or higher.

Students pursue a program of study planned in consultation with an academic advisor. The department has four graduate tracks. Each student must choose one of the four tracks. Each track has a set of 7 or 8 required courses which form the bulk of M.S. students' program of study. Students have considerable freedom in selecting elective courses in each track. See discussion of elective courses below for details. 

Unless stated otherwise, all required courses carry 3-credits. NOTE: Some first year PhD students may be required to take an ESL course.

Course Requirements for the Computational Applied Mathematics Track

Required courses for M.S. in Computational Applied Mathematics track:

  • AMS 501 Differential Equations and Boundary Value Problems (Fall)
  • AMS 503 Applications of Complex Analysis (Fall)
  • AMS 510 Analytical Methods for Applied Mathematics and Statistics (Fall)
  • AMS 526 Numerical Analysis I (Numerical Linear Algebra; Fall)
  • AMS 527 Numerical Analysis II (Approximation Theory and Numerical ODEs; Spring)
  • AMS 528 Numerical Analysis III (Numerical PDEs; Spring)
  • AMS 595 Fundamentals of Computing (Fall), or AMS 561 Introduction to Computational Science (Spring)
  • AMS 500 Responsible Conduct of Research and Scholarship (RCRS, 0 credits, required for M.S. students involved in funded research and all Ph.D. students)

plus three electives (nine credits total) from the following selection of courses:

  • AMS 502 Differential Equations and Boundary Value Problems II (Spring)
  • AMS 530 Principles in Parallel Computing (Fall)
  • AMS 542Analysis of Algorithms (Fall & Spring)
  • AMS 562  Introduction to Scientific Programming in C++ (Fall)
  • AMS 565Wave Propagation (Fall)
  • AMS 566 Compressible Fluid Dynamics (Spring)
  • AMS 603 Computational Methods for Quantitative Finance (Spring)

or other electives from AMS or other departments (such as ESE 533, MEC 539, MEC 651) with written approval from the CAM track advisor

A recommended course sequence is as follows:

First Semester (Fall)

  • AMS 501 Differential Equations and Boundary Value Problems
  • AMS 510 Analytical Methods for Applied Mathematics and Statistics (Fall)
  • AMS 526 Numerical Analysis I (Numerical Linear Algebra)
  • AMS 595 Fundamentals of Computing (If not taking an ESL course)

Second Semester (Spring)

  • AMS 502 Differential Equations and Boundary Value Problems II (or choose another elective for Masters students)
  • AMS 527 Numerical Analysis II (Approximation Theory and Numerical ODEs)
  • AMS 528 Numerical Analysis III (Numerical PDEs)
  • AMS 561 Introduction to Computational Science (if skipped AMS 595 in the Fall)
  • AMS 500 Responsible Conduct of Research and Scholarship (RCRS for M.S. students involved in funded research and all Ph.D. students

Third Semester (Fall)

Course Requirements for the Computational Biology Track

The required courses provide computational biology students with the fundamentals of both biology and applied mathematics, as well as in specific methods and applications in computational biology. It is expected that the student will choose a set of electives to provide in depth specialization.

Core Courses
Fundamentals of Applied Math

  • AMS 507 Introduction to Probability
  • AMS 510 Analytical Methods for Applied Mathematics and Statistics
  • AMS 533 Numerical Methods and Algorithms in Computational Biology

Fundamentals of Biology

  • CHE 541/MCB 520 Graduate Biochemistry (an alternate graduate level cell or developmental biology course may be substituted with permission)

Methods of Computational Biology

  • AMS 531 Laboratory Rotations in Computational Biology (2 semesters)
  • AMS 532Journal Club in Computational Biology (3 semesters)
  • AMS 535 Introduction to Computational Structural Biology and Drug Design
  • AMS 537 Biological Networks and Dynamics
  • CSE 549  Computational Biology

Electives

  • AMS 530 Principles in Parallel Computing
  • AMS 534 Introduction to Systems Biology
  • AMS 536 Molecular Modeling of Biological Molecules
  • CHE 528 Statistical Mechanics
  • CHE 523 Chemical Thermodynamics
  • PHY 558  Physical and Quantitative Biology

Typical Course Sequence for Computational Biology Track
For more information about the interdisciplinary Computaitonal Biology program, please see CompBio Website.

Course Requirements for the Operations Research Track

  • AMS 507 Introduction to Probability
  • AMS 510 Analytical Methods for Applied Mathematics and Statistics
  • AMS 540 Linear Programming
  • AMS 550 Stochastic Models
  • AMS 553/CSE 529 Simulation and Modeling
  • AMS 595 Fundamentals of Computing
  • One course in statistics (courses numbered AMS 570-586)

plus three electives from the following selection of courses

A recommended course sequence is as follows:

 First Semester (Fall):

  • AMS 507 Introduction to Probability
  • AMS 510 Analytical Methods for Applied Mathematics and Statistics
  • AMS 540 Linear Programming
  • AMS 595 Fundamentals of Computing

Second Semester (Spring):

  • AMS 550 Stochastic Models
  • One Operations Research Elective
  • One Statistics Elective

 Third Semester (Fall):

  • AMS 553 Simulation and Modeling
  • Two electives (Operations Research)

Course Requirements for the Quantitative Finance Track

The standard program of study for the M.S. degree specializing in quantitative finance consists of : 

AMS 507 Introduction to Probability
AMS 510 Analytical Methods for Applied Mathematics and Statistics
AMS 511 Foundations of Quantitative Financ
AMS 512 Portfolio Theory
AMS 513 Financial Derivatives and Stochastic Calculus
AMS 514 Computational Finance
AMS 516 Statistical Methods in Finance
AMS 517 Quantitative Risk Management
AMS 518 Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization
AMS 572 Data Analysis

Quantitative Finance Track Electives (students must take at least  2 elective courses to achieve at least  36 graduate credits along with the required courses): 

AMS 515  Case Studies in Computational Finance 
AMS 520 Machine Learning in Quantitative Finance
AMS 522  Bayesian Methods in Finance
AMS 523  Mathematics of High Frequency Finance
AMS 526  Numerical Analysis I 
AMS 527  Numerical Analysis II 
AMS 528  Numerical Analysis III 
AMS 530  Principles of Parallel Computing 
AMS 540  Linear Programming
AMS 542  Analysis of Algorithms
AMS 550  Stochastic Models
AMS 553  Simulation and Modeling
AMS 560  Big Data Systems, Algorithms and Networks
AMS 561  Introduction to Computational and Data Science
AMS 562  Introduction to Scientific Programming in C++
AMS 569  Probability Theory I
AMS 570  Introduction to Mathematical Statistics
AMS 578  Regression Theory
AMS 580  Statistical Learning
AMS 588  Failure and Survival Data Analysis
AMS 595  Fundamentals of Computing
AMS 603  Risk Measures for Finance and Data Analysis

Elective courses in the QF program are split in five focus areas. Students can follow one of the following course sequences depending upon their interests.

(A) Typical course sequence:   Modelling and risk management in finance

  • First Semester - AMS  507 ,  510 ,  511 , 572 (Elective AMS 520)
  • Second Semester - AMS  512 ,  513 ,  517 (Electives: AMS 515 , 522 , 523 , 603 )
  • Third Semester - AMS  514 ,  516 , 518 (Electives: AMS 553)

 (B) Typical course sequence:   Machine learning and big data

  • First Semester - AMS  507 ,  510 ,  511 , 572 (Elective AMS 520)
  • Second Semester - AMS  512 ,  513 ,  517 (Electives: AMS 515 , 560 , 580 )
  • Third Semester - AMS  514 ,  516 , 518 (Electives: AMS 588)

 (C) Typical course sequence:   Statistics and data analytics

  • First Semester - AMS  507 ,  510 ,  511 , 572 (Elective AMS 520)
  • Second Semester - AMS  512 ,  513 ,  517 (Electives: AMS 515 , 570 , 578 (with pre-requisite 572  )
  • Third Semester - AMS  514 ,  516 , 518 (Electives: AMS 553 , 588) 

 (D) Typical course sequence:   Stochastic calculus, optimization, and   operation research

(E) Typical course sequence: Computational methods and algorithms

  • First Semester - AMS  507 ,  510 ,  511 , 572 (Elective AMS 520)
  • Second Semester - AMS  512 ,  513 ,  517 (Electives: AMS 515 , 527 , 528 , 561 )
  • Third Semester - AMS  514 ,  516 , 518 (Electives: AMS 530 , 562 , 526 (co-requisite or pre-requisite 595 or 561 )

Note 1: If you have poor programming skills take the following electives (instead of electives recommended in sequences) : AMS 595  Fundamentals of computing (Fall semester) or AMS 561 Introduction to computational and data science (Spring semester). Programming skills are critically important for industrial jobs.

Note 2: If a 4th semester becomes necessary, a required course will be needed to continue.

For Ph.D. requirements please click here.

Quantitative Finance Opportunities for Applied Mathematics Graduate Students in Other Tracks
Any strong student (3.5+ GPA in first-semester core courses) in another track may enroll in AMS 511, Foundations in Quantitative Finance.  Selected students, with the permission of the Director of the Center for Quantitative Finance, may take additional quantitative finance courses. Students are eligible to earn an  Advanced Certificate in Quantitative Finance. You must formally apply for the secondary certificate program prior to taking the required courses. Only a maximum of six credits taken prior to enrolling in the certificate program may be used towards the requirements. Please note that credits used toward your primary program may not be used toward the certificate program. The 15-credit advanced certificate requires  AMS 511,  AMS 512,  AMS 513,  one additional Quantitative Finance Graduate course elective, and one additional Applied Mathematics course chosen with an advisor’s approval.

Course Requirements for the Statistics Track

Required Courses for M.S. Degree in Statistics Track

  • AMS 507 Introduction to Probability
  • AMS 510 Analytical Methods for Applied Mathematics and Statistics
  • AMS 570 Mathematical Statistics I
  • AMS 571 Mathematical Statistics II (required for PhD only)
  • AMS 572 Data Analysis
  • AMS 573 Design and Analysis of Categorical Data
  • AMS 578 Regression
  • AMS 582 Design of Experiments
  • AMS 597 Statistical Computing

plus two electives chosen from other graduate courses in the department or (with an advisor's approval) graduate statistics courses in other departments. The following is a list of some popular (and important) elective choices:

  • AMS 595 Fundamentals of Computing
  • AMS 586 Time Series  (*Receiving grades of B- or better in both AMS578 and AMS586 – is considered as the equivalence of the VEE Applied Statistics in the ASA Actuarial Exam.
  • AMS 598 Big Data Analysis
  • AMS 550 Stochastic Models 

Given that the track of Statistics is highly correlated with the track of Quantitative Finance (QF), interested students can choose to take selected courses in QF and obtain the Advanced Certificate in Quantitative Finance. Please see following website for detailed information.

Typical Course Sequence for Statistics Track

  • First Semester: AMS 507, 510, 572, elective
  • Second Semester: AMS 570, 573, 578, 597
  • Third Semester: AMS 582, electives (*** Ph.D. student should take AMS 571 if he/she has not done so previously)

Elective Requirements for the M.S. Degree
Any graduate-level AMS course or, with the permission of the Applied Math Graduate Program Director, graduate-level courses in a related discipline may be used to complete the 30-credit M.S. requirement in addition to the preceding core course requirement in each track. 

Time Limit
All requirements for the Master of Science degree must be completed within three years of the student's first registration as a full-time graduate study. Additional time is allowed for part-time students.

Recent M.S. Profiles