## Undergraduate Courses

### MTH 110 Introduction to Mathematics (A)

Placement for students with weak backgrounds in mathematics; Closed to students who have passed MTH 111 or 121 or higher or any statistics course. Places major emphasis on algebraic skills, basic operations on signed numbers (decimal and fractional forms): percents; techniques for solving linear and quadratic equations and systems of equations using two variables; algebraic operations on polynomials, roots and radicals. *3 Cr. Every Semester.*

### MTH 111 College Algebra (A)

*Prerequisite: Instructors approval required.*

Closed to students who have completed MTH 122 or a calculus course. Covers algebra at the intermediate level, including operations on polynomials and algebraic fractions, solution of first- and second-degree equations, graphs of functions, logarithms and exponential functions. *3 Cr. Every Semester.*

### MTH 112 College Mathematics (A,M)

*Prerequisite: MTH 110 or higher; Placement for most students with good high school mathematics background, meets Brockport General Education Mathematics course requirement.*

Develops college-level skills in algebra, geometry, data analysis, and quantitative reasoning. Practice with linear and non-linear equations, geometric problem-solving, probability, algorithms, tabular and graphic techniques, modeling real world problems. Must pass final comprehensive examination to pass course. *3 Cr. Every Semester.*

### MTH 113 Mathematics for Elementary Teachers I (A)

*Prerequisite: Any mathematics course that satisfies the College's General Education requirement in College Mathematics; Open only students seeking elementary teaching certification.*

Includes: sets, relations, number systems, elementary number theory, algebra, and mathematical systems. Uses a problem-solving approach where appropriate. *3 Cr. Every Semester.*

### MTH 114 Mathematics for Elementary Teachers II (A)

*Prerequisite: MTH 113 or any MTH course numbered 201 or higher.*

Covers various aspects of geometry, including area, volume, coordinate and transformational geometry, probability and statistics. Emphasizes problem solving and the instructional use of calculators and computers. *3 Cr. Every Semester.*

### MTH 122 Pre-Calculus (A,M)

*Prerequisite: MTH 111 or instructor's permission.Closed to students who have credit for MTH 201.*

Designed to prepare students for the study of calculus. Covers algebraic, exponential, logarithmic, and trigonometric functions. *4 Cr. Every Semester.*

### MTH 201 Calculus I (A,M)

Prerequisite: MTH 122 or Instructor's Permission.. Covers limits and continuity; derivatives and integrals of algebraic, trigonometric, exponential, and logarithmic functions; and applications of the derivative. *4 Cr. Every Semester.*

### MTH 202 Calculus II (A,M)

*Prerequisite: MTH 201.*

Covers techniques and applications of integration, approximation methods, Taylor polynomials, improper integrals, polar coordinates, and an introduction to infinite series. *4 Cr. Every Semester.*

### MTH 203 Calculus III (A,M)

*Prerequisite: MTH 202.*

Covers vectors and 3-space, functions of several variables, applications of partial derivatives, multiple integrals, and vector calculus. *4 Cr. Every Semester.*

### MTH 221 Calculus for Business, Social and Life Sciences I (A,M)

*Prerequisite: MTH 111, 121 or higher {exclude MTH 112}.*

Closed to students who have completed MTH 201 with a grade of "C" or better. Provides an introduction to calculus, with an emphasis on its applications to business and the behavioral sciences. Covers derivatives of functions of one and several variables, applied maximization and minimization problems, exponential growth and decay models, the natural logarithm function, and an introduction to integration. *3 Cr. Every Semester.*

### MTH 243 Elementary Statistics (A,M)

*Prerequisites: MTH 110 or higher {excluding MTH 112}.*

Closed to students who have received academic credit for ECN 204, MTH 244, PSH 202, SOC 200, or transfer credit for an elementary statistics course at another institution. Covers the use and limitations of various statistical concepts, including frequency distributions, measures of central tendency and of variation, use of normal curve and t-tables, sampling, estimation, tests of significance for means, and correlation. *3 Cr. Every Semester.*

### MTH 255 Differential Equations (A)

*Prerequisite: MTH 202.*

Covers first order differential equations and applications, second order and higher order linear differential equations, series solutions about ordinary points and the Laplace Transform. *3 Cr. Every Semester.*

### MTH 281 Discrete Mathematics I (B)

*Prerequisite: MTH 122 or 201/202/203.*

Provides an introduction to discrete mathematics. Includes these topics: propositional and predicate logic, sets, functions, matrix algebra, algorithms, valid arguments, direct and indirect proofs, mathematical induction, permutations and combinations, and discrete probability. *4 Cr. Every Semester.*

### MTH 324 Linear Algebra (A)

*Prerequisite: MTH 202 and MTH 281 or instructor's permission.*

Covers matrices, determinants, vector spaces and subspaces, dimension, linear transformations and Euclidean vector spaces. *3 Cr. Every Semester.*

### MTH 346 Probability and Statistics I (A)

*Prerequisites: MTH 202 and MTH 281 or instructors approval.*

Covers random variables and vectors, moments and moment generating functions, discrete and continuous probability distributions, and sampling distributions. *3 Cr. Every Semester.*

### MTH 347 R Programming for Statistics (B)

*Prerequisites: MTH 122 AND CSC 120 OR instructor permission.*

Provides an introduction to R, a widely used open-source statistical program. Students will learn basic statistical visualization and analysis in R studio, including charts and tables, data distributions, simple linear regression, estimation, and hypothesis-testing. Includes a lab component. *4 Cr. Every Semester.*

### MTH 394 Topics in Competition Problem Solving (A)

*Prerequisite: Instructor's Permission.*

Covers topics needed to solve problems in the Putnam exam and other national math competitions in the past five years. Will discuss different approaches used to solve such problems and the background theory. *1 Cr. Fall.*

### MTH 395 Research Seminar in Mathematics (A)

*Prerequisite: Instructor's Permission.*

Provides an introduction to specific research methods and techniques. Will discuss typing of mathematical documents using LATEX. Each student will be assigned a research project. Emphasizes theory and proofs in different areas. Requires extensive writing. *1-3 Cr. Spring.*

### MTH 399 Independent Study in Mathematics (A)

*Prerequisite: Instructor Permission.*

To be defined in consultation with the instructor sponsor and in accordance with the procedures of the Office of Academic Advisement prior to registration. *1-3 Cr. *

### MTH 405 Mathematical Problem Solving (A)

*Prerequisites: - MTH 202 & 281 plus Instructor's Permission.*

Develops problem-solving ability in mathematics. Includes how to get started, methods of proof, devising a strategy, and "looking back." Places strong emphasis on critical reasoning and clarity of written expression. *3 Cr. *

### MTH 412 History of Mathematics (A)

*Prerequisites: MTH 202 and MTH 281.*

Covers the history and development of mathematical ideas from primitive origins to the present. Includes topics such as arithmetic, number theory, geometries, algebra, calculus, and selected advanced topics. *3 Cr. Spring.*

### MTH 421 Number Theory (A)

*Prerequisites: MTH 202 and MTH 281.*

Topics include but are not limited to: mathematical induction, divisibility, primes, arithmetic functions, congruencies, modular arithmetic, Diophantine problems and the distribution of primes. *3 Cr. *

### MTH 423 Data Science (A)

*Prerequisites: MTH 281 & 202.*

An introduction to techniques and topics of data science. This course will cover both the mathematical background behind models in machine learning, as well as an emphasis on programming projects done in Python. Covers linear and logistic regression, classification problems, k-nearest neighbors, random forest decision trees, support vector machines and unsupervised learning. Swing course MTH 523. *3 Cr. *

### MTH 425 Modern Algebra (A)

*Prerequisites: MTH 324 with "C" or above and Instructor's Permission.*

Provides a study of algebraic systems, with special attention to groups and their classification properties. Emphasizes theory and proofs, but clarifies the ideas by means of specific examples involving modular arithmetic, real and complex numbers, permutations, and matrices.Requires extensive writing. *3 Cr. Every Semester.*

### MTH 430 Topology (A)

*Prerequisite: MTH 324.*

Provides a study of topologies on various spaces. Emphasizes theory, abstraction, proof techniques and clarifies these by means of many specific examples. Bridges topics such as geometry, analysis and algebra. Topics include, but are not limited to set theory, continuous functions, connectedness, compactness, and separation. *3 Cr. Spring.*

### MTH 432 College Geometry (A)

*Prerequisite: MTH 324.*

Provides a study of geometry from the synthetic, analytic, transformational, and vector viewpoints. Includes these topics: axiomatic systems, finite geometries, absolute geometry, Euclidean geometry, non-Euclidean geometries, geometric transformations, and projective geometry. Requires extensive writing. *3 Cr. Fall.*

### MTH 441 Statistical Methods (A)

*Prerequisites: MTH 446.*

This course focuses on investigative statistics, emphasizing the process of data collection and data analysis. It will incorporate case studies from current events and interdisciplinary research, taking a problem-based approach to learn how to determine which statistical techniques are appropriate. Topics will typically include making connections between the two-sample t-test, Regression and ANOVA; Multiple Regression; Design and Analysis of Experiments; Logistic Regression and Survival Analysis. *3 Cr. *

### MTH 446 Probability and Statistics II (A)

*Prerequisites: MTH 203 and MTH 346.*

Covers the Central Limit Theorem, maximum likelihood estimation, unbiased and sufficient statistics, minimum variance, confidence intervals, Neyman-Pearson Lemma, power calculations, and likelihood ratio tests. *3 Cr. Spring.*

### MTH 447 Time Series (A)

*Prerequisites - MTH 243 or MTH 346.*

This course introduces the theory and practice of Time Series Analysis. Students will learn how to model and forecast a time series as well as read papers from the literature. *3 Cr. *

### MTH 452 Financial Mathematics (A)

*Prerequisite: MTH 202 or 203.*

Provides fundamental concepts of financial mathematics and prepares students for EXAM FM (Financial Mathematics) of the Society of Actuaries. Students will learn about inflation, rate of interest, stocks, bonds, and other financial instruments. MTH 552 is the swing course. *3 Cr. *

### MTH 453 Actuarial Mathematics (A)

*Prerequisites: MTH 346 or instructor's permission.*

Introduces students to Actuarial Science, emphasizes the development of strong problem solving skills in preparation for the Exam P (Probability) of the Society of Actuaries. *3 Cr. *

### MTH 456 Advanced Differential Equations (A)

*Prerequisites: MTH 255, MTH 324 or some exposure to matrix theory.*

Covers series solutions about singular points, systems of linear first-order differential equations, plane autonomous systems, Fourier series, Sturm Liouville problems, partial differential equations of physics including the heat, wave and Laplace equation. *3 Cr. *

### MTH 457 Real Analysis (A)

*Prerequisites: MTH 324 with C grade or >.*

Provides a study of functions of a real variable. Emphasizes theory, proof techniques, and writing skills. Includes: real numbers, denseness of the rational numbers, convergence of sequences of real numbers, Cauchy sequences, Bolzano-Weierstrass theorem, continuous functions, uniform continuity, differentiable functions, and integrable functions. Enhances understanding of the topics through a series of required writing tasks. *3 Cr. Every Semester.*

### MTH 458 Complex Analysis (A)

*Prerequisites: MTH203 and MTH324.*

Provides a study of functions of a complex variable. Focus on the theory of analytic functions. Includes: Cauchy-Rienmann equations, Cauchy’s Theorem, Cauchy’s integral formula, the Fundamental Theorem of Algebra, Laurent series, Residue Theorem, Contour intergration and applications to real integrals. *3 Cr. *

### MTH 460 Mathematical Modeling (A)

*Prerequisites: MTH 202 and MTH 281.*

Topics covered include Linear Programs, Duality Theory and Sensitivity Analysis, Simplex Method, Integer Programs, Branch and Bound, Markov chains (Ergodic and Absorbing), Critical Path Method, Birth and Death Processes, Intro to Queuing: M/M/1 queues; M/M/1 queues with finite capacity; M/M/s queues; finite source models; general distribution service models. Optimization and Algebra software will be used. *3 Cr. *

### MTH 463 Graph Theory (A)

*Prerequisite: MTH 324 or instructor's permission.*

An introduction to graph theory, including distance concepts, symmetry and structure, trees and connectivity, Eulerian and Hamiltonian Graphs, planar graphs and imbeddings, and applications of graphs. *3 Cr. *

### MTH 465 Combinatorics (A)

*Prerequisites: MTH 324.*

An introduction to combinatorics, including basic counting techniques involving permutations, combinations, compositions, and partitions; binomial coefficients; the twelve-fold way; recursions and generating functions. Other topics may include a more advanced study of permutations, sequences in combinatorics, magic squares, the probabilistic method, etc. *3 Cr. *

### MTH 471 Numerical Analysis I (A)

*Prerequisites: MTH 203.*

Provides a survey of methods used to numerically approximate the solutions of a variety of mathematical problems. Covers the generation and propagation of round-off errors, convergence criteria, and efficiency of computation. Includes: roots of non-linear equations, systems of linear or non-linear equations, polynomial approximations, and an introduction to numerical differentiation and integration. Mathematical software, such as MAPLE, will be used. *3 Cr. *

### MTH 481 Discrete Mathematics II (A)

*Prerequisites: MTH 201 and MTH 281.*

A second course in discrete mathematics. Includes: study of algorithms, recurrence relations, inclusion-exclusion principle, partial order and equivalence relations, graph theory and trees. *3 Cr. Every Semester.*

### MTH 492 Mathematics Internship (A)

*Prerequisite: Instructor's Permission.*

Allows for a supervised experience in applying mathematical skills and techniques in a practical work environment. Requires projects that may include applications in business, the social sciences, or physical sciences. A maximum of three credits can be applied toward the mathematics major. *1-6 Cr. *

### MTH 499 Independent Study in Mathematics (A)

*Prerequisite: Instructor's Permission.*

To be defined in consultation with the instructor/sponsor and in accordance with the procedures of the Office of Academic Advisement prior to registration. *1-3 Cr. *

## Graduate Courses

### MTH 505 Mathematical Problem Solving (A)

*Prerequisite - Instructor's Permission.*

Develops problem-solving ability in mathematics. Includes how to get started, methods of proof, devising a strategy, and "looking back." Places strong emphasis on critical reasoning and clarity of written expression. *3 Cr. Summer.*

### MTH 512 History of Mathematics (A)

*Prerequisite: MTH 202 and either MTH 245 or MTH 281.*

Covers the history and development of mathematical ideas from primitive origins to today. Includes topics such as arithmetic, number theory, geometries, algebra, calculus and selected advanced topics. *3 Cr. *

### MTH 521 Number Theory (A)

*Prerequisites: MTH 202 and MTH 281.*

Topics include but are not limited to: mathematical induction, divisibility, primes, arithmetic functions, congruencies, modular arithmetic, Diophantine problems and the distribution of primes. *3 Cr. *

### MTH 523 Data Science (A)

*Prerequisites: MTH 281 & 202.*

An introduction to techniques and topics of data science. This course will cover both the mathematical background behind models in machine learning, as well as an emphasis on programming projects done in Python. Covers linear and logistic regression, classification problems, k-nearest neighbors, random forest decision trees, support vector machines and unsupervised learning. Swing course MTH 423. *3 Cr. *

### MTH 525 Modern Algebra (A)

Provides a study of algebraic systems, with special attention to groups and their classification properties. Emphasizes theory and proofs, but clarifies that ideas by means of specific examples involving modular arithmetic, real and complex numbers, permutations, and matrices. Requires extensive writing. *3 Cr. Every Semester.*

### MTH 530 Topology (A)

*Prerequisites - MTH324.*

Provides a study of topologies on various spaces. Emphasizes theory, abstraction, proof techniques and clarifies these by means of many specific examples. Bridges topics such as geometry, analysis and algebra. Topics include, but are not limited to set theory, continuous functions, connectedness, compactness, and separation. *3 Cr. Spring.*

### MTH 532 College Geometry (A)

*Prerequisite: MTH 324.*

Studies geometry from the synthetic, analytic, transformational and vector viewpoints. Includes these topics: axiomatic systems, finite geometries, absolute geometry, Euclidean geometry, non-Euclidean geometries, geometric transformations and projective geometry. *3 Cr. *

### MTH 541 Statistical Methods (A)

*Prerequisites: MTH 446 or MTH 456.*

This course focuses on investigative statistics, emphasizing the process of data collection and data analysis. It will incorporate case studies from current events and interdisciplinary research, taking a problem-based approach to learn how to determine which statistical techniques are appropriate. Topics will typically include making connections between the two-sample t-test, Regression and ANOVA; Multiple Regression; Design and Analysis of Experiments; Logistic Regression and Survival Analysis. *3 Cr. *

### MTH 546 Probability and Statistics II (A)

*Prerequisites: MTH 203 and MTH 346.*

Covers the Central Limit Theorem, maximum likelihood estimation, method of moments, unbiased and sufficient statistics, minimum variance, Cramer-Rao lower bound, confidence intervals, Neyman-Pearson Lemma, power calculations, likelihood ratio tests. *3 Cr. *

### MTH 547 Time Series (A)

*Prerequisites - MTH243 or MTH346.*

This course introduces the theory and practice of Time Series Analysis. Students will learn how to model and forecast a time series as well as read papers from the literature. *3 Cr. *

### MTH 552 Financial Mathematics (A)

Provides fundamental concepts of financial mathematics and prepares students for EXAM FM (Financial Mathematics) of the Society of Actuaries. Students will learn about inflation, rate of interest, stocks, bonds, and other financial instruments. Midterm and final exam will contain more advanced problems specifically designed for graduate students. In addition graduate students will complete a project. MTH 442 is the swing course. *3 Cr. *

### MTH 556 Advanced Differential Equations (A)

*Prerequisites: MTH 255, MTH 324 or some exposure to matrix theory.*

Covers series solutions about singular points, systems of linear first-order differential equations, plane autonomous systems, Fourier series, Sturm Liouville problems, partial differential equations of physics including the heat, wave and Laplace equation. *3 Cr. *

### MTH 557 Real Analysis (A)

*Prerequisites: MTH 203 and MTH 324.*

Provides a study of functions of a real variable. Emphasizes theory and proof techniques. Includes: real numbers, denseness of the rational numbers, convergence of sequences of real numbers, Cauchy sequences, Bolzano-Weierstrass theorem, continuous functions, uniform continuity, differentiable functions and integrable functions. Enhances understanding of the topics through a series of required writing tasks. *3 Cr. *

### MTH 558 Complex Analysis (A)

*Prerequisites: MTH203 and MTH324.*

Provides a study of functions of a complex variable. Focus on the theory of analytic functions. Includes: Cauchy-Rienmann equations, Cauchy’s Theorem, Cauchy’s integral formula, the Fundamental Theorem of Algebra, Laurent series, Residue Theorem, Contour intergration and applications to real integrals. *3 Cr. *

### MTH 560 Mathematical Modeling (A)

*Prerequisites: MTH 202 and MTH 281.*

Topics covered include Linear Programs, Duality Theory and Sensitivity Analysis, Simplex Method, Integer Programs, Branch and Bound, Markov chains (Ergodic and Absorbing), Critical Path Method, Birth and Death Processes, Intro to Queuing: M/M/1 queues; M/M/1 queues with finite capacity; M/M/s queues; finite source models; general distribution service models. Optimization and Algebra software will be used. *3 Cr. *

### MTH 563 Graph Theory (A)

*Prerequisite: MTH324 or instructor's permission.*

An introduction to graph theory, including distance concepts, symmetry and structure, trees and connectivity, Eulerian and Hamiltonian Graphs, planar graphs and imbeddings and applications of graphs. *3 Cr. *

### MTH 565 Combinatorics (A)

*Prerequisites: MTH 324 and instructor's permission.*

An introduction to combinatorics, including basic counting techniques involving permutations, combinations, compositions, and partitions; binomial coefficients; the twelve-fold way; recursions and generating functions. Other topics may include a more advanced study of permutations, sequences in combinatorics, magic squares, the probabilistic method, etc. *3 Cr. *

### MTH 571 Numerical Analysis I (A)

*Prerequisites: MTH 203.*

Covers the development of methods used to numerically approximate the solutions to mathematical problems, with consideration given to generation and propagation of round-off errors, convergence criteria and efficiency of computation. Includes these topics: roots of nonlinear equations, systems of nonlinear and linear equations, polynomial approximations, numerical differentiation and integration, and curve fitting. Mathematical software, such as MAPLE, will be used. *3 Cr. *

### MTH 581 Discrete Mathematics II (A)

*Prerequisites: MTH 201 and MTH 281.*

A second course in discrete mathematics. Includes: study of algorithms, recurrence relations, inclusion-exclusion principle, partial order and equivalence relations, graph theory, and trees. *3 Cr. *

### MTH 592 Mathematics Internship (A)

*(Prerequisite - Instructor's Permission) Allows for a supervised experience in applying mathematical skills and techniques in a practical work environment.*

Requires projects that may include applications in business, the social sciences, or physical sciences. A maximum of three credits can be applied toward the mathematics major. *1-6 Cr. Every Semester.*

### MTH 599 Independent Study in Mathematics (A)

(Prerequisite - Instructor's Permission) To be defined in consultation with the instructor/ sponsor prior to registration. *1-3 Cr. *

### MTH 605 Problem Solving in Mathematics (A)

*Prerequisite - Instructor's Permission.*

Develops problem-solving ability at the graduate level. Emphasis on meaning, strategies and written communication. Especially appropriate for adolescence mathematics teachers. *3 Cr. *

### MTH 621 Algebra (A)

*Prerequisite: MTH 425.*

Includes these topics: groups and subgroups, normal subgroups and quotient groups, permutation groups, finite Abelian groups, some special classes of rings, homomorphisms, ideals and quotient rings Euclidean rings and polynomial rings. *3 Cr. *

### MTH 628 Applications of Algebra (A)

*Prerequisite: MTH 425 and either MTH 621 or permission of instructor.*

Applies group theory and ring theory to the solution of polynomial equations and to problems in number theory, geometry, coding theory, combinatorics and selected areas of computer science. *3 Cr. *

### MTH 629 Topics in Algebra and Number Theory (A)

*Prerequisite: permission of instructor.*

Introduces topics of current interest in research or topics not covered in other courses in algebra and number theory. An outline of selected topics will be announced before the course is offered. *3 Cr. *

### MTH 639 Topics in Geometry (A)

*Prerequisite: MTH 324.*

Introduces topics of current interest in research or topics not covered in other courses in geometry. An outline of selected topics will be announced before the course is offered. *3 Cr. *

### MTH 641 Mathematical Statistics (A)

*Prerequisite: MTH 446 or MTH546.*

Allows for rigorous development of probability concepts in the sample space and models for discrete and continuous random variables. Introduces bivariate normal distribution, transformation of variables, statistics and sampling distributions, Central Limit Theorem, parametric estimation, Rao-Cramer inequality, hypothesis tests, power functions, Neyman-Pearson Theorem and both UMP and Likelihood Ratio tests. *3 Cr. *

### MTH 651 Real Analysis (A)

*Prerequisite: MTH 457.*

Includes topics such as uniform continuity and the Weierstrass Approximation Theorem, theory of differentiation and the Riemann integral, convergence of series of functions, uniform convergence of series of functions, functions of bounded variation, Riemann-Stieltjes integration, Lebesque measure and Lebesque integration. *3 Cr. *

### MTH 659 Topics in Analysis (A)

*Prerequisite: permission of instructor.*

Introduces topics of current interest in research or topics not covered in other courses in analysis. An outline of selected topics will be announced before the course is offered. *3 Cr. *

### MTH 669 Topics in Applicable Mathematics and Statistics (A)

*Prerequisite: permission of instructor.*

Introduces topics of current interest in research or topics not covered in other courses in applicable mathematics and statistics. An outline of selected topics will be announced before the course is offered. *3 Cr. *

### MTH 681 Topics in Discrete Mathematics (A)

*Prerequisite - Instructor's Permission.*

Includes topics of current interest in areas of discrete mathematics not covered (in depth) in other discrete math courses. An outline of selected topic(s) will be announced before the course begins. *3 Cr. *

### MTH 699 Independent Study in Mathematics (A)

To be defined in consultation with the instructor/sponsor prior to registration. *1-3 Cr. *