Computational Mathematics Bachelor of science degree
Computational Mathematics
Bachelor of science degree
Breadcrumb
 RIT /
 Rochester Institute of Technology /
 Academics /
 Computational Mathematics BS
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585‑475‑2163, mlrsma@rit.edu
School of Mathematical Sciences
Overview
The computational mathematics degree emphasizes problem solving using mathematical models to identify solutions 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 problemsolving tools to come up with mathematical solutions to realworld 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. Students are required to complete an experiential learning component of the program, as approved by the School of Mathematical Sciences. Students are encouraged to participate in research opportunities or cooperative education experiences. You will gain extensive computing skills through a number of highlevel programming, system design, and other computer science courses.
Nature of work
Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve economic, scientific, engineering, physics, and business problems.
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 
Cooperative Education
Cooperative education, or coop for short, is fulltime, paid work experience in your field of study. And it sets RIT graduates apart from their competitors. It’s exposure–early and often–to a variety of professional work environments, career paths, and industries. RIT coop is designed for your success.
Although cooperative education is optional for computational mathematics students, it may be used to fulfill the experiential learning component of the program. Students have worked in a variety of settings on problemsolving teams with engineers, biologists, computer scientists, physicists, and marketing specialists.
Explore salary and career information for Computational Mathematics BS
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Dr. Tony Wong
Mathematics is a powerful tool for answering questions. From mitigating climate risks to splitting the dinner bill, Professor Wong shows students that math is more than just a prerequisite.
Curriculum for Computational Mathematics BS
Computational Mathematics, BS degree, typical course sequence
Course  Sem. Cr. Hrs.  

First Year  
CSCI141 
General Education – Elective: Computer Science I
This course serves as an introduction to computational thinking using a problemcentered 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 endofterm project is also required. Lec/Lab 6 (Fall, Spring).

4 
CSCI142 
General Education – Elective: Computer Science II
This course delves further into problem solving by continuing the discussion of data structure use and design, but now from an objectoriented perspective. Key topics include more information on tree and graph structures, nested data structures, objects, classes, inheritance, interfaces, objectoriented collection class libraries for abstract data types (e.g. stacks, queues, maps, and trees), and static vs. dynamic data types. Concepts of objectoriented 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 objectoriented 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. (Prerequisites: CSCI141 with a grade of C or better or equivalent course.) Lec/Lab 6 (Fall, Spring, Summer).

4 
MATH181 
General Education – Mathematical Perspective A: ProjectBased Calculus I
This is the first in a twocourse 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. (Prerequisite: A or better in MATH111 or A or better in ((NMTH260 or NMTH272 or NMTH275) and NMTH220) or a math placement exam score greater than or equal to 70 or department permission to enroll in this class.) Lecture 6 (Fall, Spring, Summer).

4 
MATH182 
General Education – Mathematical Perspective B: ProjectBased Calculus II
This is the second in a twocourse 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. (Prerequisites: C or better in (MATH181 or MATH173 or 1016282) or (MATH171 and MATH180) or equivalent course(s).) Lecture 6 (Fall, Spring, Summer).

4 
MATH199 
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. Seminar 1 (Fall).

1 
YOPS10 
RIT 365: RIT Connections
RIT 365 students participate in experiential learning opportunities designed to launch them into their career at RIT, support them in making multiple and varied connections across the university, and immerse them in processes of competency development. Students will plan for and reflect on their firstyear experiences, receive feedback, and develop a personal plan for future action in order to develop foundational selfawareness and recognize broadbased professional competencies. Lecture 1 (Fall, Spring).

0 
General Education – Artistic Perspective 
3  
General Education – Natural Science Inquiry Perspective‡ 
4  
General Education – Elective 
3  
General Education – FirstYear Writing (WI) 
3  
Second Year  
CSCI243 
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. (Prerequisites: (CSCI140 or CSCI142 or CSCI242) with a grade of C or better or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
CSCI262 
Introduction to Computer Science Theory
This course provides an introduction to the theory of computation, including formal languages, grammars, automata theory, computability, and complexity. (Prerequisites: (MATH190 or MATH200 or 1016366) and (CSCI140 or CSCI141 or CSCI142 or CSCI242 or 4003242) or equivalent courses.) Lecture 3 (Fall, Spring, Summer).

3 
MATH200 
Discrete Mathematics and 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. (Prerequisite: MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 3, Recitation 4 (Fall).

3 
MATH231 
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. (Prerequisite: MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
MATH251 
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 realworld problems. A statistical package such as Minitab or R is used for data analysis and statistical applications. (Prerequisites: MATH173 or MATH182 or MATH 182A or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
MATH399 
Mathematical Sciences Job Search Seminar
This course helps students prepare to search for coop or fulltime 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. Lecture 1 (Fall, Spring).

0 
Choose one of the following:  4 

MATH221 
General Education – Elective: 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, vectorvalued 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 MATH219. (Prerequisite: C or better MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 4 (Fall, Spring, Summer).


MATH221H  General Education – Elective: Honors Multivariable and Vector Calculus 

Choose one of the following:  3 

MATH241 
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. (Prerequisites: MATH190 or MATH200 or MATH219 or MATH220 or MATH221 or MATH221H or equivalent course.) Lecture 3 (Fall, Spring).


MATH241H  Honors Linear Algebra 

General Education – Ethical Perspective 
3  
General Education – Global Perspective 
3  
General Education – Scientific Principles Perspective‡ 
4  
Third Year  
MATH411 
Numerical Analysis
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and the solution of initial value problems. (Prerequisites: (MATH231 and MATH241) or MATH233 or equivalent courses.) Lecture 3 (Fall).

3 
MATH431 
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. (Prerequisites: (MATH190 or MATH200 or 1055265) and (MATH220 or MATH221 or MATH221H or 1016410 or 1016328) or equivalent courses.) Lec/Lab 4 (Fall, Spring).

3 
Program Electives† 
12  
General Education – Social Perspective 
3  
General Education – Immersion 1 
3  
General Education – Elective 
3  
Open Elective 
3  
Fourth Year  
MATH421 
Mathematical Modeling (WIPR)
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. (Prerequisites: (MATH220 or MATH221 or 1016410 or 1016328) and MATH231 and MATH241 and MATH251 or equivalent courses.) Lecture 3 (Fall).

3 
MATH441 
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. (Prerequisites: (MATH190 or MATH200 or 1055265) and MATH241 or equivalent courses.) Lec/Lab 4 (Fall, Spring).

3 
Program Electives† 
6  
General Education – Immersion 2, 3 
6  
General Education – Elective Three 
3  
Open Elective 
9  
Total Semester Credit Hours  122 
Please see General Education Curriculum (GE) 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.
† Three of the program electives must be MATH or STAT courses with course numbers of at least 250, and either Graph Theory (MATH351) or Numerical Linear Algebra (MATH412) must be one of the three courses. Three of the program electives must be CSCI courses (SWEN261 is also acceptable as one of these three courses). The remaining electives can be either a CSCI, MATH, or STAT course with a course number of at least 250.
‡ Students will satisfy this requirement by taking either University Physics I (PHYS211) and University Physics II (PHYS212) or General & Analytical Chemistry I and Lab (CHMG141/145) and General & Analytical Chemistry II and Lab (CHMG142/146) or General Biology I and Lab (BIOL101/103) and General Biology II and Lab (BIOL102/104).
§ Students are required to complete an experiential learning component of the program, as approved by the School of Mathematical Sciences. Students are urged to fulfill this requirement by participating in research opportunities or coop experiences; students can also fulfill this requirement by taking MATH500 as a program elective.
Accelerated dual degree options
Accelerated dual degree options are for undergraduate students with outstanding academic records. Upon acceptance, wellqualified 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 advisor for more information.
Computational Mathematics, BS degree/Applied and Computational Mathematics (thesis option), MS degree, typical course sequence
Course  Sem. Cr. Hrs.  

First Year  
CSCI141 
General Education – Elective: Computer Science I
This course serves as an introduction to computational thinking using a problemcentered 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 endofterm project is also required. Lec/Lab 6 (Fall, Spring).

4 
CSCI142 
General Education – Elective: Computer Science II
This course delves further into problem solving by continuing the discussion of data structure use and design, but now from an objectoriented perspective. Key topics include more information on tree and graph structures, nested data structures, objects, classes, inheritance, interfaces, objectoriented collection class libraries for abstract data types (e.g. stacks, queues, maps, and trees), and static vs. dynamic data types. Concepts of objectoriented 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 objectoriented 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. (Prerequisites: CSCI141 with a grade of C or better or equivalent course.) Lec/Lab 6 (Fall, Spring, Summer).

4 
MATH181 
General Education – Mathematical Perspective A: ProjectBased Calculus I
This is the first in a twocourse 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. (Prerequisite: A or better in MATH111 or A or better in ((NMTH260 or NMTH272 or NMTH275) and NMTH220) or a math placement exam score greater than or equal to 70 or department permission to enroll in this class.) Lecture 6 (Fall, Spring, Summer).

4 
MATH182 
General Education – Mathematical Perspective B: ProjectBased Calculus II
This is the second in a twocourse 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. (Prerequisites: C or better in (MATH181 or MATH173 or 1016282) or (MATH171 and MATH180) or equivalent course(s).) Lecture 6 (Fall, Spring, Summer).

4 
MATH199 
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. Seminar 1 (Fall).

1 
YOPS10 
RIT 365: RIT Connections
RIT 365 students participate in experiential learning opportunities designed to launch them into their career at RIT, support them in making multiple and varied connections across the university, and immerse them in processes of competency development. Students will plan for and reflect on their firstyear experiences, receive feedback, and develop a personal plan for future action in order to develop foundational selfawareness and recognize broadbased professional competencies. Lecture 1 (Fall, Spring).

0 
General Education – Artistic Perspective 
3  
General Education – Natural Science Inquiry Perspective‡ 
4  
General Education – Elective 
3  
General Education – FirstYear Writing (WI) 
3  
Open Elective 
3  
Second Year  
CSCI243 
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. (Prerequisites: (CSCI140 or CSCI142 or CSCI242) with a grade of C or better or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
CSCI262 
Introduction to Computer Science Theory
This course provides an introduction to the theory of computation, including formal languages, grammars, automata theory, computability, and complexity. (Prerequisites: (MATH190 or MATH200 or 1016366) and (CSCI140 or CSCI141 or CSCI142 or CSCI242 or 4003242) or equivalent courses.) Lecture 3 (Fall, Spring, Summer).

3 
MATH200 
Discrete Mathematics and 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. (Prerequisite: MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 3, Recitation 4 (Fall).

3 
MATH231 
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. (Prerequisite: MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
MATH251 
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 realworld problems. A statistical package such as Minitab or R is used for data analysis and statistical applications. (Prerequisites: MATH173 or MATH182 or MATH 182A or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
MATH399 
Mathematical Sciences Job Search Seminar
This course helps students prepare to search for coop or fulltime 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. Lecture 1 (Fall, Spring).

0 
Choose one of the following:  4 

MATH221 
General Education – Elective: 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, vectorvalued 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 MATH219. (Prerequisite: C or better MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 4 (Fall, Spring, Summer).


MATH221H  General Education – Elective: Honors Multivariable and Vector Calculus 

Choose one of the following:  3 

MATH241 
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. (Prerequisites: MATH190 or MATH200 or MATH219 or MATH220 or MATH221 or MATH221H or equivalent course.) Lecture 3 (Fall, Spring).


MATH241H  Honors Linear Algebra 

General Education – Ethical Perspective 
3  
General Education – Global Perspective 
3  
General Education – Scientific Principles Perspective‡ 
4  
Third Year  
MATH431 
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. (Prerequisites: (MATH190 or MATH200 or 1055265) and (MATH220 or MATH221 or MATH221H or 1016410 or 1016328) or equivalent courses.) Lec/Lab 4 (Fall, Spring).

3 
MATH441 
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. (Prerequisites: (MATH190 or MATH200 or 1055265) and MATH241 or equivalent courses.) Lec/Lab 4 (Fall, Spring).

3 
Program Electives 
12  
General Education – Social Perspective 
3  
General Education – Immersion 1, 2 
6  
General Education – Elective 
3  
Fourth Year  
MATH421 
Mathematical Modeling (WIPR)
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. (Prerequisites: (MATH220 or MATH221 or 1016410 or 1016328) and MATH231 and MATH241 and MATH251 or equivalent courses.) Lecture 3 (Fall).

3 
MATH602 
Numerical Analysis I
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra. (Prerequisites: (MATH241 and MATH431) or equivalent courses or graduate standing in ACMTHMS or MATHMLPHD programs.) Lecture 3 (Fall).

3 
MATH606 
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. (This course is restricted to students in the ACMTHMS or MATHMLPHD programs.) Lecture 2 (Fall).

1 
MATH607 
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. (Prerequisite: MATH606 or equivalent course or students in the ACMTHMS or MATHMLPHD programs.) Lecture 2 (Spring).

1 
Math Graduate Core Courses 
6  
Open Electives 
9  
General Education – Immersion 3 
3  
General Education – Elective 
3  
Program Elective 
3  
Fifth Year  
MATH790 
Research & Thesis
Masterslevel research by the candidate on an appropriate topic as arranged between the candidate and the research advisor. (This course is restricted to students in the ACMTHMS or MATHMLPHD programs.) Thesis (Fall, Spring, Summer).

7 
MATH Graduate Electives 
12  
Total Semester Credit Hours  146 
Please see General Education Curriculum (GE) 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 4credit 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.
Computational Mathematics, BS degree/Applied and Computational Mathematics (project option), MS degree, typical course sequence
Course  Sem. Cr. Hrs.  

First Year  
CSCI141 
General Education – Elective: Computer Science I
This course serves as an introduction to computational thinking using a problemcentered 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 endofterm project is also required. Lec/Lab 6 (Fall, Spring).

4 
CSCI142 
General Education – Elective: Computer Science II
This course delves further into problem solving by continuing the discussion of data structure use and design, but now from an objectoriented perspective. Key topics include more information on tree and graph structures, nested data structures, objects, classes, inheritance, interfaces, objectoriented collection class libraries for abstract data types (e.g. stacks, queues, maps, and trees), and static vs. dynamic data types. Concepts of objectoriented 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 objectoriented 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. (Prerequisites: CSCI141 with a grade of C or better or equivalent course.) Lec/Lab 6 (Fall, Spring, Summer).

4 
MATH181 
General Education – Mathematical Perspective A: ProjectBased Calculus I
This is the first in a twocourse 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. (Prerequisite: A or better in MATH111 or A or better in ((NMTH260 or NMTH272 or NMTH275) and NMTH220) or a math placement exam score greater than or equal to 70 or department permission to enroll in this class.) Lecture 6 (Fall, Spring, Summer).

4 
MATH182 
General Education – Mathematical Perspective B: ProjectBased Calculus II
This is the second in a twocourse 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. (Prerequisites: C or better in (MATH181 or MATH173 or 1016282) or (MATH171 and MATH180) or equivalent course(s).) Lecture 6 (Fall, Spring, Summer).

4 
MATH199 
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. Seminar 1 (Fall).

1 
YOPS10 
RIT 365: RIT Connections
RIT 365 students participate in experiential learning opportunities designed to launch them into their career at RIT, support them in making multiple and varied connections across the university, and immerse them in processes of competency development. Students will plan for and reflect on their firstyear experiences, receive feedback, and develop a personal plan for future action in order to develop foundational selfawareness and recognize broadbased professional competencies. Lecture 1 (Fall, Spring).

0 
General Education – Artistic Perspective 
3  
General Education – Natural Science Inquiry Perspective‡ 
4  
General Education – Elective 
3  
General Education – FirstYear Writing (WI) 
3  
Open Elective 
3  
Second Year  
CSCI243 
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. (Prerequisites: (CSCI140 or CSCI142 or CSCI242) with a grade of C or better or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
CSCI262 
Introduction to Computer Science Theory
This course provides an introduction to the theory of computation, including formal languages, grammars, automata theory, computability, and complexity. (Prerequisites: (MATH190 or MATH200 or 1016366) and (CSCI140 or CSCI141 or CSCI142 or CSCI242 or 4003242) or equivalent courses.) Lecture 3 (Fall, Spring, Summer).

3 
MATH200 
Discrete Mathematics and 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. (Prerequisite: MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 3, Recitation 4 (Fall).

3 
MATH231 
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. (Prerequisite: MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
MATH251 
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 realworld problems. A statistical package such as Minitab or R is used for data analysis and statistical applications. (Prerequisites: MATH173 or MATH182 or MATH 182A or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
MATH399 
Mathematical Sciences Job Search Seminar
This course helps students prepare to search for coop or fulltime 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. Lecture 1 (Fall, Spring).

0 
Choose one of the following:  4 

MATH221 
General Education – Elective: 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, vectorvalued 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 MATH219. (Prerequisite: C or better MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 4 (Fall, Spring, Summer).


MATH221H  General Education – Elective: Honors Multivariable and Vector Calculus 

Choose one of the following:  3 

MATH241 
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. (Prerequisites: MATH190 or MATH200 or MATH219 or MATH220 or MATH221 or MATH221H or equivalent course.) Lecture 3 (Fall, Spring).


MATH241H  Honors Linear Algebra 

General Education – Ethical Perspective 
3  
General Education – Global Perspective 
3  
General Education – Scientific Principles Perspective‡ 
4  
Third Year  
MATH431 
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. (Prerequisites: (MATH190 or MATH200 or 1055265) and (MATH220 or MATH221 or MATH221H or 1016410 or 1016328) or equivalent courses.) Lec/Lab 4 (Fall, Spring).

3 
MATH441 
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. (Prerequisites: (MATH190 or MATH200 or 1055265) and MATH241 or equivalent courses.) Lec/Lab 4 (Fall, Spring).

3 
Program Electives 
12  
General Education – Social Perspective 
3  
General Education – Immersion 1, 2 
6  
General Education – Elective 
3  
Fourth Year  
MATH421 
Mathematical Modeling (WIPR)
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. (Prerequisites: (MATH220 or MATH221 or 1016410 or 1016328) and MATH231 and MATH241 and MATH251 or equivalent courses.) Lecture 3 (Fall).

3 
MATH602 
Numerical Analysis I
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra. (Prerequisites: (MATH241 and MATH431) or equivalent courses or graduate standing in ACMTHMS or MATHMLPHD programs.) Lecture 3 (Fall).

3 
MATH606 
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. (This course is restricted to students in the ACMTHMS or MATHMLPHD programs.) Lecture 2 (Fall).

1 
MATH607 
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. (Prerequisite: MATH606 or equivalent course or students in the ACMTHMS or MATHMLPHD programs.) Lecture 2 (Spring).

1 
Math Graduate Core Courses 
6  
Open Electives 
9  
General Education – Immersion 3 
3  
General Education – Elective 
3  
Program Elective 
3  
Fifth Year  
MATH790 
Research & Thesis
Masterslevel research by the candidate on an appropriate topic as arranged between the candidate and the research advisor. (This course is restricted to students in the ACMTHMS or MATHMLPHD programs.) Thesis (Fall, Spring, Summer).

4 
MATH Graduate Electives 
15  
Total Semester Credit Hours  146 
Please see General Education Curriculum (GE) 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 4credit 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.
Computational Mathematics, BS degree/Computer Science, MS degree, typical course sequence
Course  Sem. Cr. Hrs.  

First Year  
CSCI141 
General Education – Elective: Computer Science I
This course serves as an introduction to computational thinking using a problemcentered 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 endofterm project is also required. Lec/Lab 6 (Fall, Spring).

4 
CSCI142 
General Education – Elective: Computer Science II
This course delves further into problem solving by continuing the discussion of data structure use and design, but now from an objectoriented perspective. Key topics include more information on tree and graph structures, nested data structures, objects, classes, inheritance, interfaces, objectoriented collection class libraries for abstract data types (e.g. stacks, queues, maps, and trees), and static vs. dynamic data types. Concepts of objectoriented 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 objectoriented 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. (Prerequisites: CSCI141 with a grade of C or better or equivalent course.) Lec/Lab 6 (Fall, Spring, Summer).

4 
MATH181 
General Education – Mathematical Perspective A: ProjectBased Calculus I
This is the first in a twocourse 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. (Prerequisite: A or better in MATH111 or A or better in ((NMTH260 or NMTH272 or NMTH275) and NMTH220) or a math placement exam score greater than or equal to 70 or department permission to enroll in this class.) Lecture 6 (Fall, Spring, Summer).

4 
MATH182 
General Education – Mathematical Perspective B: ProjectBased Calculus II
This is the second in a twocourse 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. (Prerequisites: C or better in (MATH181 or MATH173 or 1016282) or (MATH171 and MATH180) or equivalent course(s).) Lecture 6 (Fall, Spring, Summer).

4 
MATH199 
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. Seminar 1 (Fall).

1 
YOPS10 
RIT 365: RIT Connections
RIT 365 students participate in experiential learning opportunities designed to launch them into their career at RIT, support them in making multiple and varied connections across the university, and immerse them in processes of competency development. Students will plan for and reflect on their firstyear experiences, receive feedback, and develop a personal plan for future action in order to develop foundational selfawareness and recognize broadbased professional competencies. Lecture 1 (Fall, Spring).

0 
General Education – Artistic Perspective 
3  
General Education – Natural Science Inquiry Perspective 
4  
General Education – Elective 
3  
General Education – FirstYear Writing (WI) 
3  
Second Year  
CSCI243 
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. (Prerequisites: (CSCI140 or CSCI142 or CSCI242) with a grade of C or better or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
CSCI262 
Introduction to Computer Science Theory
This course provides an introduction to the theory of computation, including formal languages, grammars, automata theory, computability, and complexity. (Prerequisites: (MATH190 or MATH200 or 1016366) and (CSCI140 or CSCI141 or CSCI142 or CSCI242 or 4003242) or equivalent courses.) Lecture 3 (Fall, Spring, Summer).

3 
MATH200 
Discrete Mathematics and 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. (Prerequisite: MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 3, Recitation 4 (Fall).

3 
MATH231 
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. (Prerequisite: MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
MATH251 
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 realworld problems. A statistical package such as Minitab or R is used for data analysis and statistical applications. (Prerequisites: MATH173 or MATH182 or MATH 182A or equivalent course.) Lecture 3 (Fall, Spring, Summer).

3 
MATH399 
Mathematical Sciences Job Search Seminar
This course helps students prepare to search for coop or fulltime 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. Lecture 1 (Fall, Spring).

0 
Choose one of the following:  4 

MATH221 
General Education – Elective: 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, vectorvalued 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 MATH219. (Prerequisite: C or better MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 4 (Fall, Spring, Summer).


MATH221H  General Education – Elective: Honors Multivariable and Vector Calculus 

Choose one of the following:  3 

MATH241 
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. (Prerequisites: MATH190 or MATH200 or MATH219 or MATH220 or MATH221 or MATH221H or equivalent course.) Lecture 3 (Fall, Spring).


MATH241H  Honors Linear Algebra 

General Education – Ethical Perspective 
3  
General Education – Global Perspective 
3  
General Education – Scientific Principles Perspective 
4  
Third Year  
MATH411 
Numerical Analysis
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and the solution of initial value problems. (Prerequisites: (MATH231 and MATH241) or MATH233 or equivalent courses.) Lecture 3 (Fall).

3 
MATH431 
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. (Prerequisites: (MATH190 or MATH200 or 1055265) and (MATH220 or MATH221 or MATH221H or 1016410 or 1016328) or equivalent courses.) Lec/Lab 4 (Fall, Spring).

3 
Program Electives 
12  
General Education – Social Perspective 
3  
General Education – Immersion 1 
3  
General Education – Elective 
3  
Open Elective 
3  
Fourth Year  
CSCI664 
Computational Complexity
This course provides an introduction to computational complexity theory. It covers the P=NP problem, time and space complexity, randomization, approximability, and relativization. Course offered every other year. (Prerequisites: (CSCI661 or CSCI660 or CSCI262 or CSCI263) and (CSCI665 or CSCI261 or CSCI264) or equivalent courses.) Lecture 3 (Spring).

3 
CSCI665 
Foundations of Algorithms
This course provides an introduction to the design and analysis of algorithms. It covers a variety of classical algorithms and their complexity and will equip students with the intellectual tools to design, analyze, implement, and evaluate their own algorithms. Note: students who take CSCI261 or CSCI264 may not take CSCI665 for credit. (Prerequisites: (CSCI603 and CSCI605 and CSCI661 with grades of B or better) or ((CSCI243 or SWEN262) and (CSCI262 or CSCI263)) or equivalent courses. This course is restricted to COMPSCIMS, COMPSCIBS/MS, or COMPISPHD students.) Lec/Lab 3 (Fall, Spring).

3 
MATH421 
Mathematical Modeling (WIPR)
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. (Prerequisites: (MATH220 or MATH221 or 1016410 or 1016328) and MATH231 and MATH241 and MATH251 or equivalent courses.) Lecture 3 (Fall).

3 
MATH441 
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. (Prerequisites: (MATH190 or MATH200 or 1055265) and MATH241 or equivalent courses.) Lec/Lab 4 (Fall, Spring).

3 
Open Electives 
9  
General Education – Immersion 2, 3 
6  
General Education – Elective 
3  
Fifth Year  
CSCI610 
Fundamentals of Computer Graphics
Foundations of Computer Graphics is a study of the hardware and software principles of interactive raster graphics. Topics include an introduction to the basic concepts, 2D and 3D modeling and transformations, viewing transformations, projections, rendering techniques, graphical software packages and graphics systems. The course will focus on rasterization techniques and emphasize the hardware rasterization pipeline including the use of hardware shaders. Students will use a standard computer graphics API to reinforce concepts and study fundamental computer graphics algorithms. Programming projects and a survey of the current graphics literature will be required. Note: students who complete CSCI510 may not take CSCI610 for credit. (Prerequisite: (CSCI603 or CSCI605 with a grade of B or better) or (CSCI243 or SWEN262). May not take and receive credit for CSCI610 and CSCI510. If earned credit for/or currently enrolled in CSCI510 you will not be permitted to enroll in CSCI610.) Lecture 3 (Fall, Spring).

3 
CSCI630  Foundations of Artificial Intelligence 
3 
CSCI631 
Foundations of Computer Vision
An introduction to the underlying concepts of computer vision and image understanding. The course will consider fundamental topics, including image formation, edge detection, texture analysis, color, segmentation, shape analysis, detection of objects in images and high level image representation. Depending on the interest of the class, more advanced topics will be covered, such as image database retrieval or robotic vision. Programming assignments are an integral part of the course. Note: students who complete CSCI431 may not take CSCI631 for credit. (Prerequisites:(CSCI603 and CSCI605 and CSCI661 with grades of B or better) or ((CSCI243 or SWEN262) and (CSCI262 or CSCI263)) or equiv courses. If earned credit for/or currently enrolled in CSCI431 you will not be permitted to enroll in CSCI631.Prerequisites:(CSCI603 and CSCI605 and CSCI661 with grades of B or better) or ((CSCI243 or SWEN262) and (CSCI262 or CSCI263)) or equiv courses. If earned credit for/or currently enrolled in CSCI431 you will not be permitted to enroll in CSCI631.) Lecture 3 (Fall, Spring).

3 
CSCI635 
Introduction to Machine Learning
This course offers an introduction to supervised machine learning theories and algorithms, and their application to classification and regression tasks. Topics include: Mathematical background of machine learning (e.g. statistical analysis and visualization of data), neural models (e.g. Convolutional Neural Networks, Recurrent Neural Networks), probabilistic graphical models (e.g. Bayesian networks, Markov models), and reinforcement learning. Programming assignments are required. (Prerequisites: CSCI331 or CSCI630 or equivalent course.) Lecture 3 (Fall, Spring).

3 
CSCI790 
Computer Science MS Thesis
Thesis capstone of the master's degree program. Student must submit an acceptable thesis proposal in order to enroll. It is expected that the work would lead to a paper of the caliber of those generally acceptable to a national conference. (Enrollment in this course requires permission from the department offering the course.) Thesis (Fall, Spring, Summer).

6 
CSCI799 
Computer Science Graduate Independent Study
Students work with a supervising faculty member on topics of mutual interest. A student works with a potential faculty sponsor to draft a proposal that describes what a student plans to do, what deliverables are expected, how the student's work will be evaluated, and how much credit will be assigned for successful completion of the work. The faculty sponsor proposes the grade, but before the grade is officially recorded, the student must submit a final report that summarizes what was actually accomplished. (Enrollment in this course requires permission from the department offering the course.) Ind Study (Fall, Spring, Summer).

6 
Total Semester Credit Hours  146 
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, 34 years of mathematics, 23 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; precalculus 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, cost, and financial aid
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