Mathematics Minor
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 Mathematics Minor
Overview for Mathematics Minor
The mathematics minor is designed for students who want to learn new skills and develop new ways of framing and solving problems. It offers students the opportunity to explore connections among mathematical ideas and to further develop mathematical ways of thinking.
Notes about this minor:
 This minor is closed to students majoring in applied mathematics or computational mathematics.
 Posting of the minor on the student's academic transcript requires a minimum GPA of 2.0 in the minor.
 Notations may appear in the curriculum chart below outlining prerequisites, corequisites, and other curriculum requirements (see footnotes).
 At least nine semester credit hours of the minor must consist of specific courses not required by the student’s degree program.
The plan code for Mathematics Minor is MATHMN.
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Curriculum for 20242025 for Mathematics Minor
Current Students: See Curriculum Requirements
Course  

Prerequisites  
Students must complete:  
MATH181  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. (Prerequisites: MATH111 or (NMTH220 and NMTH260 or NMTH272 or NMTH275) or equivalent courses with a minimum grade of B, or a score of at least 60% on the RIT Mathematics Placement Exam.) Lecture 4 (Fall, Spring). 
or  
MATH181A  Calculus I This is the first in a twocourse sequence intended for students majoring in mathematics, science, or engineering. The course includes the same topics as MATH181, but the focus of the workshop component is different. Whereas workshops attached to 181 emphasize concept development and realworld applications, the workshops of MATH181A emphasize skill development and provide justintime review of precalculus material as needed. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals. (Prerequisite: B or better in MATH111 or B or better in ((NMTH260 or NMTH272 or NMTH275) and NMTH220) or a math placement exam greater than or equal to 60.) Lecture 6 (Fall, Spring). 
or both the following:  
MATH171  Calculus A This is the first course in a threecourse sequence (COSMATH171, 172, 173). This course includes a study of precalculus, polynomial, rational, exponential, logarithmic and trigonometric functions, continuity, and differentiability. Limits of functions are used to study continuity and differentiability. The study of the derivative includes the definition, basic rules, and implicit differentiation. Applications of the derivative include optimization and relatedrates problems. (Prerequisites: Completion of the math placement exam or C or better in MATH111 or C or better in ((NMTH260 or NMTH272 or NMTH275) and NMTH220) or equivalent course.) Lecture 5 (Fall, Spring). 
MATH172  Calculus B This is the second course in threecourse sequence (COSMATH171, 172, 173). The course includes Riemann sums, the Fundamental Theorem of Calculus, techniques of integration, and applications of the definite integral. The techniques of integration include substitution and integration by parts. The applications of the definite integral include areas between curves, and the calculation of volume. (Prerequisites: C or better in MATH171 or 1016171T or 1016281 or 1016231 or equivalent course.) Lecture 5 (Fall, Spring). 
plus one of the following:  
MATH182  Calculus II (or equivalent) This is the second in a twocourse sequence. 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 MATH181A or equivalent course.) Lecture 4 (Fall, Spring). 
MATH190  Discrete Mathematics for Computing This course introduces students to ideas and techniques from discrete mathematics that are widely used in Computer Science. Students will learn about the fundamentals of propositional and predicate calculus, set theory, relations, recursive structures and counting. This course will help increase students’ mathematical sophistication and their ability to handle abstract problems. (Corequisites: MATH182 or MATH182A or MATH172 or equivalent courses.) Lecture 3, Recitation 1 (Fall, Spring). 
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: MATH182 or equivalent course.) Lecture 3, Recitation 4 (Fall, Spring). 
Electives  
Choose five of the following, with at least one course from Group II, at least two courses must be at the 300level or higher, and at least three courses must not be required by the student's major:  
Group I  
MATH219  Multivariable Calculus* This course is principally a study of the calculus of functions of two or more variables, but also includes the study of vectors, vectorvalued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, and includes applications in physics. Credit cannot be granted for both this course and MATH221. (Prerequisite: C or better MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 3 (Fall, Spring, Summer). 
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. (Prerequisite: C or better MATH173 or MATH182 or MATH182A or equivalent course.) Lecture 4 (Fall, Spring, Summer). 
MATH221H  Honors Multivariable and Vector Calculus* This course is an honors version of MATH221. It includes an introduction to vectors, surfaces, and multivariable functions. It covers limits, partial derivatives and differentiability, multiple integrals, Stokes’ Theorem, Green’s Theorem, the Divergence Theorem, and applications. Unlike MATH221, students in this course will often be expected to learn elementary skills and concepts from their text so that inclass discussion can focus primarily on extending techniques, interpreting results, and exploring mathematical topics in greater depth; homework exercises and projects given in this class will require greater synthesis of concepts and skills, on average, than those in MATH221. Students earning credit for this course cannot earn credit for MATH219 or MATH221. (Prerequisites: C or better in MATH182 or MATH173 or MATH182A and Honors program status or at least a 3.2 cumulative GPA.) Lecture 4 (Fall). 
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, Recitation 1 (Fall, Spring, Summer). 
MATH233  Linear Systems and Differential Equations† This is an introductory course in linear algebra and ordinary differential equations in which a scientific computing package is used to clarify mathematical concepts, visualize problems, and work with large systems. The course covers matrix algebra, the basic notions and techniques of ordinary differential equations with constant coefficients, and the physical situation in which they arise. (Prerequisites: MATH172 or MATH182 or MATH182A and students in CHEMBS or CHEMBS/MS or ISEEBS programs.) Lecture 4 (Spring). 
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‡ This honors course introduces the basic concepts and techniques of linear algebra. Concepts are addressed at a higher level than the standard course in linear algebra, and the topic list is somewhat broader. Topics include linear independence and span, linear functions, solving systems of linear equations using Gaussian elimination, the arithmetic and algebra of matrices, basic properties and interpretation of determinants, vector spaces, the fundamental subspaces of a linear function, eigenvalues and eigenvectors, change of basis, similarity and diagonalization. Students will learn to communicate explanations of mathematical facts and techniques by participating in a collaborative workshop format, and will learn to use MATLAB to solve matrix equations. (Prerequisites: MATH219 or MATH221 or MATH221H or equivalent course and Honors program status or at least a 3.2 cumulative GPA.) Lecture 3 (Spring). 
MATH251  Probability and Statistics 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, Recitation 1 (Fall, Spring, Summer). 
MATH301  Mathematics of Simulation & Randomness This course is an introduction to mathematical techniques and algorithms for (pseudo)random number generation and simulation. Randomness and simulation are major tools used in mathematical modeling, statistical and data analysis, computing, and engineering. This course will provide both a solid mathematical foundation in these topics and computational experience utilizing them in practice. (Prerequisites: (MATH190 or MATH200) and MATH251 and (GCIS123 or CSCI141) or equivalent courses.) Lecture 3 (Fall). 
MATH311  Linear Optimization This course presents the general linear programming problem. Topics include a review of pertinent matrix theory, convex sets and systems of linear inequalities, the simplex method of solution, artificial bases, duality, parametric programming, and applications. (Prerequisites: MATH241 or MATH241H or equivalent course.) Lecture 3 (Spring). 
MATH312  Nonlinear Optimization This course provides a study of the theory of optimization of nonlinear functions of several variables with or without constraints. Applications of this theory in business, management, engineering and the sciences are considered. Algorithms for practical applications will be analyzed and implemented. The course may require the use of specialized software to analyze problems. Students taking this course will be expected to complete applied projects and/or case studies. (Prerequisites: (MATH219 or MATH221 or MATH221H) and MATH311 or equivalent course.) Lecture 3 (Spring). 
MATH321  Classical Game Theory Classical game theory models conflict and cooperation between rational decisionmaking agents with hidden parameters. Topics include matrix games, Nash equilibria, the minimax theorem, prisoner’s dilemma, and cooperative games. Applications can include adaptive or statistical decision theory, artificial intelligence (online learning, multiagent systems), biology (evolutionary games, signaling behavior, fighting behavior), economics and business (auctions, bankruptcy, bargaining, pricing, twosided markets), philosophy (ethics, morality, social norms), and political science (apportionment, elections, military strategy, stability of government, voting). (Prerequisites: MATH241 or MATH241H or equivalent course.) Lecture 3 (Fall). 
MATH322  Combinatorial Game Theory Combinatorial games are twoplayer games with perfect information and no randomness or element of chance (such as Go, Chess, and Checkers). The course covers basic techniques of game theory, outcome classes, sums of games, the algebra of games, and topdown induction. Analyses will emphasize nodraw games terminating in a finite number of moves such as Nim, Domineering, Hackenbush, Chomp, and Amazons. (Prerequisites: MATH190 or MATH200 or equivalent course.) Lecture 3 (Fall). 
MATH326  Boundary Value Problems This course provides an introduction to boundary value problems. Topics include Fourier series, separation of variables, Laplace's equation, the heat equation, and the wave equation in Cartesian and polar coordinate systems. (Prerequisites: (MATH231 or MATH233) and (MATH219 or MATH221) or equivalent courses.) Lecture 3 (Fall, Spring). 
MATH331  Dynamical Systems The course revisits the equations of springmass system, RLC circuits, and pendulum systems in order to view and interpret the phase space representations of these dynamical systems. The course begins with linear systems followed by a study of the stability analysis of nonlinear systems. Matrix techniques are introduced to study higher order systems. The Lorentz equation will be studied to introduce the concept of chaotic solutions. (Prerequisites: (MATH231 and (MATH241 or MATH241H)) or MATH233 or equivalent courses.) Lecture 3 (Spring). 
MATH361  Combinatorics This course introduces the mathematical theory of enumeration of discrete structures. Topics include enumeration, combinatorial proofs, recursion, inclusionexclusion, and generating functions. (Prerequisites: MATH190 or MATH200 or equivalent course.) Lecture 3 (Spring). 
MATH367  Codes and Ciphers This course will introduce, explain and employ both the classical and modern basic techniques of cryptography. Topics will include the Vignère cipher, affine ciphers, Hill ciphers, onetime pad encryption, Enigma, public key encryption schemes (RSA, DiffieHellman, ElGamal, elliptic curves), and hash functions. The course will include an introduction to algebraic structures and number theoretic tools used in cryptography. (Prerequisites: MATH190 or MATH200 or equivalent course.) Lecture 3 (Spring). 
MATH367H  Honors Codes and Ciphers The course introduces students to basic techniques of classical and modern cryptography, and learn about the significant impact of codes and ciphers on historical events. Topics will include the Vignère cipher, affine ciphers, Hill ciphers, onetime pad encryption, Enigma, public key encryption schemes (RSA, DiffieHellman, elliptic curves), and cryptographic hash functions. The course will include an introduction to algebraic structures and number theoretic tools used in cryptography. Students in this honors course will also study and explore historical source documents to get firsthand exposure to critical aspects of cryptanalysis from the early to mid20th century. (Prerequisites: MATH190 or MATH200 or equivalent course and Honors program status or at least a 3.3 cumulative GPA.) Lecture 3 (Fall). 
MATH381  Complex Variables This course covers the algebra of complex numbers, analytic functions, CauchyRiemann equations, complex integration, Cauchy's integral theorem and integral formulas, Taylor and Laurent series, residues, and the calculation of realvalued integrals by complexvariable methods. (Prerequisites: MATH219 or MATH221 or equivalent course.) Lecture 3 (Fall, Spring). 
Group II  
MATH341  Advanced Linear Algebra This is a second course in linear algebra that provides an indepth study of fundamental concepts of the subject. It focuses largely on the effect that a choice of basis has on our understanding of and ability to solve problems with linear operators. Topics include linear transformations, similarity, inner products and orthogonality, QR factorization, singular value decomposition, and the Spectral Theorem. The course includes both computational techniques and the further development of mathematical reasoning skills. (Prerequisites: MATH241 or MATH241H or equivalent course.) Lecture 3 (Spring, Summer). 
MATH351  Graph Theory This course covers the theory of graphs and networks for both directed and undirected graphs. Topics include graph isomorphism, Eulerian and Hamiltonian graphs, matching, covers, connectivity, coloring, and planarity. There is an emphasis on applications to real world problems and on graph algorithms such as those for spanning trees, shortest paths, and network flows. (Prerequisites: MATH190 or MATH200 or equivalent course.) Lecture 3 (Fall). 
MATH371  Number Theory This course provides an introduction to the study of the set of integers and their algebraic properties. Topics include prime factorization and divisibility, linear Diophantine equations, congruences, arithmetic functions, primitive roots, and quadratic residues. (Prerequisites: MATH190 or MATH200 or equivalent course.) Lecture 3 (Spring). 
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 MATH241H)) or MATH233 or equivalent courses.) Lecture 3 (Fall). 
MATH412  Numerical Linear Algebra This course covers numerical techniques for the solution of systems of linear equations, eigenvalue problems, singular values and other decompositions, applications to least squares, boundary value problems, and additional topics at the discretion of the instructor. (Prerequisites: (MATH220 or MATH221 or MATH221H or 1055359 (Honors Multivariable Calculus)) and (MATH231 and MATH341) or equivalent courses.) Lecture 3 (Spring). 
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). 
MATH432  Real Variables II This course is a continuation of MATH431. It concentrates on differentiation, integration (Riemann and RiemannStieltjes integrals), power series, and sequences and series of functions. (Prerequisites: MATH431 or equivalent course) Lecture 3 (Spring). 
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 MATH241H) or equivalent courses.) Lec/Lab 4 (Fall, Spring). 
MATH442  Abstract Algebra II This course covers the basic theory of rings, integral domains, ideals, modules, and abstract vector spaces. It also covers the key constructions including direct sums, direct products, and field extensions. These topics serve as the foundation of mathematics behind advanced topics such as algebraic geometry and various applications like cryptography and coding theory. (Prerequisites: MATH441 or equivalent course.) Lecture 3 (Spring). 
MATH461  Topology This course defines metric spaces and topological spaces. For metric spaces it examines continuity spaces of continuous functions and completeness in Euclidean spaces. For topological spaces it examines compactness, continuous functions, and separation axioms. (Prerequisites: MATH432 or equivalent course.) Lecture 3 (Spring). 
MATH505  Stochastic Processes This course explores Poisson processes and Markov chains with an emphasis on applications. Extensive use is made of conditional probability and conditional expectation. Further topics, such as renewal processes, Brownian motion, queuing models and reliability are discussed as time allows. (Prerequisites: (MATH241 or MATH241H) and MATH251 or equivalent courses.) Lecture 3 (Spring). 
* Students may choose only one of these courses, but no more.
† Students may choose only one of these courses, but not both.
‡ Students may choose only one of these courses, but not both.
Contact
 Hossein Shahmohamad
 Professor
 School of Mathematics and Statistics
 College of Science
 mathminor@rit.edu
School of Mathematics and Statistics