Computational Mathematics Bachelor of science degree

936cab1b-2068-44f5-8acc-689181f8ae31 | 85991

Overview

An emphasis on using computers as tools to solve mathematically modeled physical problems in business, science, engineering, and more.


The computational mathematics major combines the beauty and logic of mathematics with the application of today’s fastest and most powerful computers. The major uses computers as problem-solving tools to come up with mathematical solutions to real-world problems in engineering, operations research, economics, business and other areas of science. The skills you learn can be applied to everyday life, from computing security and telecommunication networking to routes for school buses and delivery companies. The computational mathematics major gives you a solid foundation in both mathematics and computational methods that you need to be successful in the field or in graduate school.

Computational mathematics prepares you for a mathematical career that incorporates extensive computer science skills. In this major, much emphasis is given to the use of the computer as a tool to solve mathematically modeled physical problems. Students often pursue positions as mathematical analysts, scientific programmers, software engineers, or systems analysts. Job opportunities in private industry and government abound in this field.

Course of Study

The curriculum provides a foundation in mathematics through courses in calculus, differential equations, graph theory, abstract and linear algebra, mathematical modeling, numerical analysis, and several other areas. You will gain extensive computing skills through a number of high-level programming, system design, and other computer science courses.

Real World Experiences

Although cooperative education is optional for computational mathematics students, many participate for three or more months in paid, professional co-op positions before graduation. Students have worked in a variety of settings on problem-solving teams with engineers, biologists, computer scientists, physicists, and marketing specialists. For more information and co-op listings, visit the RIT Office of Cooperative Education and Career Services.

Nature of Work

Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve economic, scientific, engineering, physics, and business problems.

Advantages

Computational mathematics majors may complete a dual degree in as little as one extra year of study. You can complete a BS in computational mathematics and an MS in computer science to give you an edge over many computer science majors entering the workforce. You may also combine a BS in computational mathematics with an MS in applied and computational mathematics.

Industries


  • Insurance

  • Government (Local, State, Federal)

  • Internet and Software

  • Defense

  • Electronic and Computer Hardware

  • Manufacturing

Typical Job Titles

Software Engineer Computer Scientist
Analyst (e.g. Operations Research) Cryptanalyst (codes)
Actuary Market Researcher
Financial Advisor

80%

outcome rate of graduates

$65k

median first-year salary of graduates

Latest News

Curriculum

Computational mathematics, BS degree, typical course sequence

Course Sem. Cr. Hrs.
First Year
MATH-181
LAS Perspective 7A (mathematical): Project-based Calculus I
This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals.
4
MATH-182
LAS Perspective 7B (mathematical): Project-based Calculus II
This is the second in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates.
4
MATH-199
Mathematics and Statistics Seminar
This course introduces the programs within the School of Mathematical Sciences, and provides an introduction to math and statistics software. The course provides practice in technical writing.
1
CSCI-141
Computer Science I
This course serves as an introduction to computational thinking using a problem-centered approach. Specific topics covered include: expression of algorithms in pseudo code and a programming language; functional and imperative programming techniques; control structures; problem solving using recursion; basic searching and sorting; elementary data structures such as lists, trees, and graphs; and correctness, testing and debugging. Assignments (both in class and for homework) requiring a pseudo code solution and an implementation are an integral part of the course. An end-of-term project is also required.
4
CSCI-142
Computer Science II
This course delves further into problem solving by continuing the discussion of data structure use and design, but now from an object-oriented perspective. Key topics include more information on tree and graph structures, nested data structures, objects, classes, inheritance, interfaces, object-oriented collection class libraries for abstract data types (e.g. stacks, queues, maps, and trees), and static vs. dynamic data types. Concepts of object-oriented design are a large part of the course. Software qualities related to object orientation, namely cohesion, minimal coupling, modifiability, and extensibility, are all introduced in this course, as well as a few elementary object-oriented design patterns. Input and output streams, graphical user interfaces, and exception handling are covered. Students will also be introduced to a modern integrated software development environment (IDE). Programming projects will be required.
4
ACSC-010
Year One
The Year One class serves as an interdisciplinary catalyst for first-year students to access campus resources, services and opportunities that promote self-knowledge, personal success, leadership development, social responsibility and life academic skills awareness and application. Year One is also designed to challenge and encourage first-year students to get to know one another, build relationships and help them become an integral part of the campus community.
0
 
LAS Perspective 1 (ethical)
3
 
LAS Perspective 5‡ (natural science inquiry)
4
 
First Year LAS Elective
3
 
First Year Writing (WI)
3
 
Wellness Education*
0
Second Year
MATH-221
Multivariable and Vector Calculus
This course is principally a study of the calculus of functions of two or more variables, but also includes a study of vectors, vector-valued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, Stokes' Theorem, Green's Theorem, the Divergence Theorem, and applications in physics. Credit cannot be granted for both this course and MATH-219.
4
MATH-251
Probability and Statistics I
This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab or R is used for data analysis and statistical applications.
3
MATH-231
Differential Equations
This course is an introduction to the study of ordinary differential equations and their applications. Topics include solutions to first order equations and linear second order equations, method of undetermined coefficients, variation of parameters, linear independence and the Wronskian, vibrating systems, and Laplace transforms.
3
MATH-241
Linear Algebra
This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course.
3
CSCI-243
The Mechanics of Programming
Students will be introduced to the details of program structure and the mechanics of execution as well as supportive operating system features. Security and performance issues in program design will be discussed. The program translation process will be examined. Programming assignments will be required.
3
MATH-200
Discrete Mathematics with Introduction to Proofs
This course prepares students for professions that use mathematics in daily practice, and for mathematics courses beyond the introductory level where it is essential to communicate effectively in the language of mathematics. It covers various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and set theory, and then moving to applications in advanced mathematics.
3
CSCI-262
Introduction to Computer Science Theory
This course provides an introduction to the theory of computation, including formal languages, grammars, auto-mata theory, computability, and complexity.
3
MATH-399
Mathematical Science Job Search Seminar
This course helps students prepare to search for co-op or full-time employment. Students will learn strategies for conducting a successful job search and transitioning into the work world. The course meets one hour each week for five weeks.
0
 
LAS Perspective 2 (artistic)
3
 
LAS Perspective 3 (global)
3
 
LAS Perspective 6‡ (scientific principles)
4
Third Year
MATH-431
Real Variables I
This course is an investigation and extension of the theoretical aspects of elementary calculus. Topics include mathematical induction, real numbers, sequences, functions, limits, and continuity. The workshop will focus on helping students develop skill in writing proofs.
3
MATH-411
Numerical Analysis
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and the solution of initial value problems.
3
 
Program Electives†
12
 
LAS Perspective 4 (social)
3
 
LAS Immersion 1
3
 
LAS Elective
3
 
Open Elective
3
Fourth Year
MATH-421
Mathematical Modeling (WI)
This course explores problem solving, formulation of the mathematical model from physical considerations, solution of the mathematical problem, testing the model and interpretation of results. Problems are selected from the physical sciences, engineering, and economics.
3
MATH-441
Abstract Algebra
This course covers basic set theory, number theory, groups, subgroups, cyclic and permutation groups, Lagrange and Sylow theorems, quotient groups, and isomorphism theorems. Group Theory finds applications in other scientific disciplines like physics and chemistry.
3
 
Program Electives†
12
 
LAS Immersion 2, 3
6
 
LAS Elective
3
 
Open Elective
3
Total Semester Credit Hours
122

(WI) Refers to a writing intensive course within the major.

* Please see Wellness Education Requirement for more information. Students completing bachelor's degrees are required to complete two different Wellness courses.

† Four of the program electives must be MATH or STAT courses with course numbers of at least 250, and either Graph Theory (MATH-351) or Numerical Linear Algebra (MATH-412) must be one of the four courses.

‡ Students will satisfy this requirement by taking either a 3 or 4 credit hour lab science course. If a science course consists of separate lecture and laboratory sections, the student MUST take both the lecture and lab portions to satisfy the requirement. The lecture alone will not fulfill the requirement.

Accelerated dual degree options

Accelerated dual degree options are for undergraduate students with outstanding academic records. Upon acceptance, well-qualified undergraduate students can begin graduate study before completing their BS degree, shortening the time it takes to earn both degrees. Students should consult an academic adviser for more information.

Computational mathematics, BS degree/Applied and computational mathematics, MS degree, typical course sequence

Course Sem. Cr. Hrs.
First Year
MATH-181
LAS Perspective 7A (mathematical): Project-Based Calculus I
This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals.
4
MATH-182
LAS Perspective 7B (mathematical): Project-Based Calculus II
This is the second in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates.
4
MATH-199
Mathematics and Statistics Seminar
This course introduces the programs within the School of Mathematical Sciences, and provides an introduction to math and statistics software. The course provides practice in technical writing.
1
CSCI-141
Computer Science I
This course serves as an introduction to computational thinking using a problem-centered approach. Specific topics covered include: expression of algorithms in pseudo code and a programming language; functional and imperative programming techniques; control structures; problem solving using recursion; basic searching and sorting; elementary data structures such as lists, trees, and graphs; and correctness, testing and debugging. Assignments (both in class and for homework) requiring a pseudo code solution and an implementation are an integral part of the course. An end-of-term project is also required.
4
CSCI-142
Computer Science II
This course delves further into problem solving by continuing the discussion of data structure use and design, but now from an object-oriented perspective. Key topics include more information on tree and graph structures, nested data structures, objects, classes, inheritance, interfaces, object-oriented collection class libraries for abstract data types (e.g. stacks, queues, maps, and trees), and static vs. dynamic data types. Concepts of object-oriented design are a large part of the course. Software qualities related to object orientation, namely cohesion, minimal coupling, modifiability, and extensibility, are all introduced in this course, as well as a few elementary object-oriented design patterns. Input and output streams, graphical user interfaces, and exception handling are covered. Students will also be introduced to a modern integrated software development environment (IDE). Programming projects will be required.
4
ACSC-010
Year One
The Year One class serves as an interdisciplinary catalyst for first-year students to access campus resources, services and opportunities that promote self-knowledge, personal success, leadership development, social responsibility and life academic skills awareness and application. Year One is also designed to challenge and encourage first-year students to get to know one another, build relationships and help them become an integral part of the campus community.
0
 
LAS Perspective 1 (ethical)
3
 
LAS Perspective 5‡ (natural science inquiry)
4
 
First Year LAS Elective
3
 
First Year Writing (WI)
3
 
Wellness Education*
0
 
Open Elective
3
Second Year
MATH-221
Multivariable and Vector Calculus
This course is principally a study of the calculus of functions of two or more variables, but also includes a study of vectors, vector-valued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, Stokes' Theorem, Green's Theorem, the Divergence Theorem, and applications in physics. Credit cannot be granted for both this course and MATH-219.
4
MATH-241
Linear Algebra
This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course.
3
MATH-251
Probability and Statistics I
This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab or R is used for data analysis and statistical applications.
3
MATH-231
Differential Equations
This course is an introduction to the study of ordinary differential equations and their applications. Topics include solutions to first order equations and linear second order equations, method of undetermined coefficients, variation of parameters, linear independence and the Wronskian, vibrating systems, and Laplace transforms.
3
MATH-200
Discrete Mathematics with Introduction to Proofs
This course prepares students for professions that use mathematics in daily practice, and for mathematics courses beyond the introductory level where it is essential to communicate effectively in the language of mathematics. It covers various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and set theory, and then moving to applications in advanced mathematics.
3
CSCI-243
Mechanics of Programming
Students will be introduced to the details of program structure and the mechanics of execution as well as supportive operating system features. Security and performance issues in program design will be discussed. The program translation process will be examined. Programming assignments will be required.
3
CSCI-262
Introduction to Computer Science Theory
This course provides an introduction to the theory of computation, including formal languages, grammars, auto-mata theory, computability, and complexity.
3
MATH-399
Mathematical Science Job Search Seminar
This course helps students prepare to search for co-op or full-time employment. Students will learn strategies for conducting a successful job search and transitioning into the work world. The course meets one hour each week for five weeks.
0
 
LAS Perspective 2 (artistic)
3
 
LAS Perspective 3 (global)
3
 
LAS Perspective 6‡ (scientific principles)
4
Third Year
MATH-431
Real Variables I
This course is an investigation and extension of the theoretical aspects of elementary calculus. Topics include mathematical induction, real numbers, sequences, functions, limits, and continuity. The workshop will focus on helping students develop skill in writing proofs.
3
MATH-441
Abstract Algebra I
This course covers basic set theory, number theory, groups, subgroups, cyclic and permutation groups, Lagrange and Sylow theorems, quotient groups, and isomorphism theorems. Group Theory finds applications in other scientific disciplines like physics and chemistry.
3
 
Program Electives
12
 
LAS Perspective 4 (social)
3
 
LAS Immersion 1, 2
6
 
LAS Elective
3
Fourth Year
MATH-421
Mathematical Modeling (WI)
This course explores problem solving, formulation of the mathematical model from physical considerations, solution of the mathematical problem, testing the model and interpretation of results. Problems are selected from the physical sciences, engineering, and economics.
3
MATH-606
Graduate Seminar I
The course prepares students to engage in activities necessary for independent mathematical research and introduces students to a broad range of active interdisciplinary programs related to applied mathematics.
1
MATH-607
Graduate Seminar II
This course is a continuation of Graduate Seminar I. It prepares students to engage in activities necessary for independent mathematical research and introduces them to a broad range of active interdisciplinary programs related to applied mathematics.
1
MATH-602
Numerical Analysis
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra.
3
 
Math Graduate Core
6
 
Open Electives
6
 
LAS Immersion 3
3
 
LAS Elective
3
 
Program Electives
6
Fifth Year
MATH-790
Thesis
Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.
7
 
Math Graduate Core
3
 
Concentration Core Courses
6
 
Graduate Electives
9
Total Semester Credit Hours
152

Please see General Education Curriculum–Liberal Arts and Sciences (LAS) for more information.

(WI) Refers to a writing intensive course within the major.

* Please see Wellness Education Requirement for more information. Students completing bachelor's degrees are required to complete two different Wellness courses.

‡ Students will satisfy this requirement by taking either a 3- or 4-credit hour lab science course. If a science course consists of separate lecture and laboratory sections, the student MUST take both the lecture and lab portions to satisfy the requirement. The lecture alone will not fulfill the requirement.

Admission Requirements

Freshman Admission

For all bachelor’s degree programs, a strong performance in a college preparatory program is expected. Generally, this includes 4 years of English, 3-4 years of mathematics, 2-3 years of science, and 3 years of social studies and/or history.

Specific math and science requirements and other recommendations

  • 3 years of math required; pre-calculus recommended

Transfer Admission

Transfer course recommendations without associate degree

Courses in liberal arts, physics, math, and chemistry

Appropriate associate degree programs for transfer

AS degree in liberal arts with math/science option

Learn about admissions and financial aid