Computational Mathematics Bachelor of science degree
Computational Mathematics
Bachelor of science degree
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 Computational Mathematics BS
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School of Mathematical Sciences
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 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. You will gain extensive computing skills through a number of highlevel 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 coop positions before graduation. Students have worked in a variety of settings on problemsolving teams with engineers, biologists, computer scientists, physicists, and marketing specialists. For more information and coop listings, visit the RIT Office of Career Services and Cooperative Education.
Nature of work
Mathematicians use mathematical theory, computational techniques, algorithms, and the latest computer technology to solve economic, scientific, engineering, physics, and business problems.
Accepted Student Open House
Come and meet your fellow Tigers and get the information you need and the support you want.
Saturday, March 28  Saturday, April 4
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 
Curriculum
Computational Mathematics, BS degree, typical course sequence
Course  Sem. Cr. Hrs.  

First Year  
CSCI141 
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.

4 
CSCI142 
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.

4 
MATH181 
LAS Perspective 7A (mathematical): 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.

4 
MATH182 
LAS Perspective 7B (mathematical): 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.

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.

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.

0 
LAS Perspective 1 (ethical) 
3  
LAS Perspective 5‡ (natural science inquiry) 
4  
LAS Elective 
3  
First Year Writing (WI) 
3  
Wellness Education* 
0  
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.

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.

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.

3 
MATH221 
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.

4 
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.

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.

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.

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.

0 
LAS Perspective 2 (artistic) 
3  
LAS Perspective 3 (global) 
3  
LAS Perspective 6‡ (scientific principles) 
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.

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.

3 
Program Electives† 
12  
LAS Perspective 4 (social) 
3  
LAS Immersion 1 
3  
LAS Elective 
3  
Free Elective 
3  
Wellness Education* 
0  
Fourth Year  
MATH421 
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 
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.

3 
Program Electives† 
12  
LAS Immersion 2, 3 
6  
LAS Elective 
3  
Free Elective 
3  
Total Semester Credit Hours  122 
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.
† Four 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 four 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 adviser 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 
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.

4 
CSCI142 
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.

4 
MATH181 
LAS Perspective 7A (mathematical): 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.

4 
MATH182 
LAS Perspective 7B (mathematical): 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.

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.

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.

0 
LAS Perspective 1 (ethical) 
3  
LAS Perspective 5‡ (natural science inquiry) 
4  
LAS Elective 
3  
First Year Writing (WI) 
3  
Wellness Education* 
0  
Free 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.

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.

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.

3 
MATH221 
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.

4 
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.

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.

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.

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.

0 
LAS Perspective 2 (artistic) 
3  
LAS Perspective 3 (global) 
3  
LAS Perspective 6‡ (scientific principles) 
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.

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.

3 
Program Electives 
12  
LAS Perspective 4 (social) 
3  
LAS Immersion 1, 2 
6  
LAS Elective 
3  
Wellness Education* 
0  
Fourth Year  
MATH421 
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 
MATH602 
Numerical Analysis I
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra.

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.

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.

1 
Math Graduate Core Courses 
6  
Free Electives 
6  
LAS Immersion 3 
3  
LAS Elective 
3  
Program Electives 
6  
Fifth Year  
MATH790 
Research & Thesis
Masterslevel research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.

7 
Math Graduate Core Course 
3  
Graduate Electives 
9  
Total Semester Credit Hours  146 
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 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 
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.

4 
CSCI142 
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.

4 
MATH181 
LAS Perspective 7A (mathematical): 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.

4 
MATH182 
LAS Perspective 7B (mathematical): 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.

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.

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.

0 
LAS Perspective 1 (ethical) 
3  
LAS Perspective 5‡ (natural science inquiry) 
4  
LAS Elective 
3  
First Year Writing (WI) 
3  
Wellness Education* 
0  
Free 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.

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.

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.

3 
MATH221 
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.

4 
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.

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.

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.

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.

0 
LAS Perspective 2 (artistic) 
3  
LAS Perspective 3 (global) 
3  
LAS Perspective 6‡ (scientific principles) 
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.

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.

3 
Program Electives 
12  
LAS Perspective 4 (social) 
3  
LAS Immersion 1, 2 
6  
LAS Elective 
3  
Wellness Education* 
0  
Fourth Year  
MATH421 
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 
MATH602 
Numerical Analysis I
This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and matrix algebra.

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.

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.

1 
Math Graduate Core Courses 
6  
Free Electives 
6  
LAS Immersion 3 
3  
LAS Elective 
3  
Program Electives 
6  
Fifth Year  
MATH790 
Research & Thesis
Masterslevel research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.

4 
Math Graduate Core Course 
3  
Graduate Electives 
12  
Total Semester Credit Hours  146 
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 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 
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.

4 
CSCI142 
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.

4 
MATH181 
LAS Perspective 7A (mathematical): 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.

4 
MATH182 
LAS Perspective 7B (mathematical): 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.

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.

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.

0 
LAS Perspective 1 (ethical) 
3  
LAS Perspective 5‡ (natural science inquiry) 
4  
LAS Elective 
3  
First Year Writing (WI) 
3  
Wellness Education* 
0  
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.

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.

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.

3 
MATH221 
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.

4 
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.

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.

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.

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.

0 
LAS Perspective 2 (artistic) 
3  
LAS Perspective 3 (global) 
3  
LAS Perspective 6‡ (scientific principles) 
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.

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.

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.

3 
Program Electives 
12  
LAS Perspective 4 (social) 
3  
LAS Immersion 1 
3  
LAS Elective 
3  
Wellness Education* 
0  
Fourth Year  
MATH421 
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 
Free Electives 
6  
LAS Immersion 2, 3 
6  
LAS Elective 
3  
Program Electives 
12  
Fifth Year  
CSCI630 
Foundations of Intelligent Systems
An introduction to the theories and algorithms used to create artificial intelligence (AI) systems. Topics include search algorithms, logic, planning, machine learning, and applications from areas such as computer vision, robotics, and natural language processing. Programming assignments and oral/written summaries of research papers are required.

3 
CSCI662 
Foundations of Cryptography
This course provides an introduction to cryptography, its mathematical foundations, and its relation to security. It covers classical cryptosystems, privatekey cryptosystems (including DES and AES), hashing and publickey cryptosystems (including RSA). The course also provides an introduction to data integrity and authentication. Note: students who complete CSCI462 may not take CSCI662 for credit.

3 
CSCI761 
Topics in Advanced Algorithms
This course focuses on advanced algorithms and data structures in a specialized area of computer science or in a specific scientific domain. Both practical and theoretical aspects of algorithms will be explored to provide coverage of the state of the art and shortcomings of computing in the specialized area. This includes proofs of correctness and complexity analysis of the algorithms. Students will write a term paper that explores the current state of research in the area or reports on the student's implementation and experiments with algorithms for a chosen problem. Students will also be required to make presentations. The instructor will post the specifics of each course offering before the registration. With the approval of the program coordinator, this course can be taken for credit more than once, provided each instance concerns a different specialized area or domain.

3 
CSCI762 
Advanced Cryptography
This course investigates advanced topics in cryptography. It begins with an overview of necessary background in algebra and number theory, private and publickey cryptosystems, and basic signature schemes. The course will cover number theory and basic theory of Galois fields used in cryptography; history of primality algorithms and the polynomialtime test of primality; discrete logarithm based cryptosystems including those based on elliptic curves; interactive protocols including the role of zeroknowledge proofs in authentication; construction of untraceable electronic cash on the net; and quantum cryptography, and one or more of digital watermarking, fingerprinting and stenography. Programming will be required.

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.

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.

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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