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**MAT 097
BASIC MATHEMATICS
0, 3/0**

Provides the necessary mathematics background needed to pass college-level algebra; covers polynomials, rational expressions, exponents and roots, solving equations, and inequalities.

**MAT 098
BASIC MATHEMATICS
0, 0/0**

Computer-based instruction presentation. Information is presented primarily by computer program with instructor intervention. Instructor interacts with the program by evaluating pre-tests and placing students appropriately in the course continuum. Students are encouraged to complete the entire course of study, but may exit the course when they achieve a score at or above the minimum competency exam. One hour per week attendance is required.

**MAT 103
INTRODUCTION TO CONTEMPORARY MATHEMATICS
3, 3/0; MQIF**

Some of the greatest achievements of mathematical thought, highlighting the beauty and creativity of these ideas. Topics include Fibonacci numbers, the golden rectangle, estimation, comparing infinities, fractals, the Pythagorean Theorem, the five platonic solids, and selected topics from probability and statistics. Designed for liberal arts majors who do not plan on taking further math courses.

**MAT 114
FUNCTIONS AND MODELING
3, 3/0; MQIF**

*Prerequisite: Three years high school mathematics or equivalent.*

Describe and explore real-world functions, data, and phenomena through graphic, numeric, symbolic, and verbal representations. Use elementary functions (linear, polynomial, power, and exponential) to investigate and analyze applied problems (supported by the use of appropriate technology).

**MAT 121
ELEMENTARY MATHEMATICS FROM AN ADVANCED STANDPOINT I
3, 3/0**

*Prerequisite: Three years of Regents high school mathematics or equivalent.*

First course of a two-semester sequence on the fundamental concepts of elementary mathematics: positional numeration systems, number and operations, proportional reasoning, and number theory. Emphasis on problem solving, understanding the concepts and procedures of elementary mathematics, mathematical modeling, the use of manipulatives, and effective communication of mathematical ideas. Offered every semester.

**MAT 122****ELEMENTARY MATHEMATICS FROM AN ADVANCED STANDPOINT II
3, 3/0; MQIF**

*Prerequisite: MAT 121.*

Second course of a two-semester sequence on the fundamental concepts of elementary mathematics: 2- and 3-dimensional geometry, measurement, probability, statistics, linear and non-linear functions. Emphasis on problem solving, understanding the concepts and procedures of elementary mathematics, mathematical modeling, the use of manipulatives, and effective communication of mathematical ideas. Offered every semester.

**MAT 124****FUNCTIONS AND MODELING II
3, 3/0**

*Prerequisite: MAT 114 with a minimum grade of C, or equivalent. **A precalculus course designed for students who have completed a minimum of three years of New York State Regents high school mathematics or the equivalent.*

Topics include analysis of polynomial, rational, exponential, logarithmic, and trigonometric functions from graphical, symbolic, numerical, and verbal perspectives, with an emphasis on modeling and applications of those functions in real-world contexts. No credit given to students who have previously completed MAT 126 or MAT 161 or equivalent.

**MAT 126
APPLIED CALCULUS I
4, 4/0; MQIF**

*Prerequisite: MAT 124 with a minimum grade of C, or equivalent.*

Intuitive introduction to differential and integral calculus. Analysis of functions, derivatives of algebraic, exponential, ad logarithmic functions; applications of the derivative; antiderivatives of simple algebraic, exponential and logarithmic functions, area and the fundamental theorem of calculus. Graphical, symbolic, numerical, and verbal representations are used for all topics. Designed for students majoring in disciplines that use calculus as a tool. No credit given to students who have previously completed MAT 161 or equivalent.

**MAT 127
APPLIED CALCULUS II
4, 4/0**

*Prerequisite: MAT 126 with a minimum grade of C or equivalent. Continuation of MAT 126.*

Techniques of integration; applications of integration; introduction to differential equations, including separation of variables, firstorder linear equations, and their applications; Taylor polynomials; Newton’s method; partial derivatives; and optimization of functions of two and three variables. Graphical, symbolic, numerical, and verbal representations are used for all topics. Designed for students majoring in disciplines that use calculus as a tool. Credit issued for either MAT 127 or MAT 162 (or equivalents), but not for both.

**MAT 161
CALCULUS I
4, 4/0; MQIF**

*Prerequisite: MAT 124 with a minimum grade of C, or equivalent. Corequisite: MAT 163.*

Graphic, symbolic, and numeric representation and analysis of functions; limits; continuity; derivatives and antiderivatives of algebraic, trigonometric, exponential, and logarithmic functions; applications of the derivative and antiderivative. Appropriate for math majors and students in partner disciplines requiring understanding of fundamental principles of calculus, with emphasis on deductive reasoning and proof.

**MAT 162
CALCULUS II
4, 4/0**

*Prerequisite: MAT 161 with a minimum grade of C, or equivalent. Corequisite: MAT 164.*

Area accumulation functions, definition of the definite integral, fundamental theorem of calculus, integration techniques, applications of integrals, improper integrals, sequences and series, function approximation. Graphic, symbolic, and numeric representations are used throughout the course. Appropriate for math majors and students in partner disciplines requiring understanding of fundamental principles of calculus, with emphasis on deductive reasoning and proof. Credit issued for either MAT 127 or MAT 162 (or equivalents), but not for both.

**MAT 163
USING TECHNOLOGY TO EXPLORE CALCULUS I
1, 1/0**

*Prerequisite or corequisite: MAT 161 or equivalent.*

Exploration of Calculus I using a programmable graphing calculator.

**MAT 164
USING TECHNOLOGY TO EXPLORE CALCULUS II
1, 1/0**

*Prerequisite or corequisite: MAT 162 or equivalent.*

Exploration of Calculus II, using a computer algebra system.

**MAT 202
INTRODUCTION TO LINEAR ALGEBRA
3, 3/0**

*Prerequisite: MAT 161 or MAT 126.*

Vectors and vector spaces; linear dependence, basis, and dimension; matrices and determinants; linear systems; linear transformations; eigenvectors; invariant subspaces.

**MAT 241
COMPUTER MATHEMATICS I
3, 3/0**

*Prerequisites: MAT 161, MAT 163 or equivalent or permission of instructor.*

Fundamental concepts of problem solving by computer as applied to mathematics. Computer organization, operations and functions, algorithm development, programming techniques. Numerical methods as used in calculus, linear algebra, geometry, etc. Uses a computer language to be applied in this and other mathematics classes.

**MAT 263
CALCULUS III
3, 3/0**

*Prerequisite: MAT 162. Corequisite: MAT 264.*

Multivariable spaces and functions, multivariable derivatives, multivariable integrals, and vector analysis. Offered every semester.

**MAT 264****USING TECHNOLOGY TO EXPLORE CALCULUS III
1, 1/0**

*Prerequisite: MAT 164. Prerequisite or corequisite: MAT 263.*

Exploration of Calculus III using a computer algebra system.

**MAT 270
DISCRETE MATHEMATICS I
3, 3/0**

*Prerequisite: MAT 161 or MAT 126.*

Fundamental principles used in discrete mathematics. Topics include logic, mathematical induction, sets, relations, functions, permutations, combinations, recursion, and graph theory. Offered every semester.

**MAT 300****TECHNIQUES OF PROOF
3, 3/0**

*Prerequisite: MAT 161 AND MAT 270. *

A gateway to upper-division mathematics with an emphasis on mathematical structures, techniques of proof, and the effective written and oral communication of mathematical ideas. Designed to ease the transition from lower-division mathematics to more theoretical courses such as abstract algebra and real analysis. Students are required to submit written work and make oral presentations. Offered every semester.

**MAT 301****FUNDAMENTALS OF ABSTRACT ALGEBRA
3, 3/0**

*Prerequisite: MAT 202 and MAT 300. *

Fundamental concepts of abstract algebra: sets, mappings, binary operations, relations; algebraic structures of groups, rings, fields, and applications. Offered every semester.

**MAT 302****ABSTRACT ALGEBRA II
3, 3/0**

*Prerequisite: MAT 301.*

Quotient fields of integral domains, polynomials, rings; Euclidean domains, ideals, and factorization; finite fields, extension fields, splitting fields. Applications to geometric constructions and solvability chosen from contemporary areas of coding theory, block designs, etc.

**MAT 304
GAMES AND LINEAR PROGRAMMING
3, 3/0**

*Prerequisite: Three years of Regents high school mathematics.*

Elementary techniques for finding optimal choices among game strategies and in linear programming problems using the fundamental minimax theorem and the simplex method. Applications in such areas as business, industry, economics, social sciences, and behavioral sciences. Not open to mathematics, applied mathematics, or mathematics education majors.

**MAT 306
PROBLEM SOLVING IN BASIC
3, 3/0**

*Prerequisite: Three years of Regents high school mathematics.*

Introduction to the mathematical uses of computers in today’s society. Background; typical uses; writing programs to solve problems in number theory, geometry, finance, and algebra; mathematical games; sorting. Not applicable toward mathematics major requirements.

**MAT 309
DISCRETE MATHEMATICS II
3, 3/0**

*Prerequisite: MAT 270.*

Automata, modules, group codes, linear machines, polynomial rings, cyclic codes, minimum polynomials, context-free grammars, tree automata, polish notation, pushdown automata.

**MAT 311
INTRODUCTORY PROBABILITY AND STATISTICS
3, 3/0; MQIF**

*Prerequisite: Three years of Regents high school mathematics.*

Descriptive statistics; probability and random variables; binomial, normal, and t distributions; estimation and tests of hypotheses concerning means, proportions, and differences between means and proportions. Does not count toward the mathematics, applied mathematics, or mathematics education majors.

**MAT 315
DIFFERENTIAL EQUATIONS
3, 3/0**

*Prerequisite: MAT 263 or permission of instructor.*

Preliminary ideas on order, degree, and solutions; formation of differential equations; differential equations of first-order linear equations with constant coefficients; special high-order equations; simultaneous equations; linear equations of the second order; series solutions.

**MAT 316
INTERMEDIATE DIFFERENTIAL EQUATIONS
3, 3/0**

*Prerequisite: MAT 315.*

Laplace transform; inverse Laplace transform and applications; partial differential equations; Fourier series; boundary value problems; transform methods application.

**MAT 322
MODERN GEOMETRY
3, 3/0**

*Prerequisite: MAT 270.*

Euclidean constructions; theorems of Menelaus and Ceva; crossratio; harmonic points; orthogonal circles; isometrics and similarities in the plane; introduction of projective geometry.

**MAT 325
PROBABILITY AND STATISTICS
3, 3/0**

*Prerequisites: For BS-NS MTS majors: MAT 270, MAT 162. For education majors with mathematics concentrations: MAT 127 or MAT 162; MAT 270 and MAT 311; or permission of instructor.*

Probability (graphic representations, descriptions of probabilistic events, combinatorics, and combinatorial probability); discrete and continuous probability distributions; descriptive statistics; estimation and tests of hypotheses concerning means, proportions, variance and standard deviation, and differences between means and proportions.

**MAT 351
ELEMENTARY THEORY OF NUMBERS
3, 3/0**

*Prerequisite: Four years of Regents high school mathematics.*

Divisibility; Euclid’s algorithm; numbers; prime factorization theorem; Euler’s phi-function; Diophantine analysis; congruence; theorems of Fermat, Euler, and Wilson.

**MAT 366
COMPUTER MATHEMATICS II
3, 3/0**

*Prerequisites: MAT 164, MAT 241, MAT 270; or permission of instructor.*

Structured programming, verification of program validity, data structures, combinatorial problems, flow network, algorithms, random-number generators, simulation of random and nonrandom processes.

**MAT 370
APPLIED NETWORKS
3, 3/0**

*Prerequisites: MAT 202, MAT 270.*

Introduction to network and graph theoretic concepts. Properties with application in computational mathematics, social science, decision making, and physical science.

**MAT 381
PROBABILITY
3, 3/0**

*Prerequisites: MAT 270; MAT 127 or MAT 162.*

Probability models; discrete and continuous random variables and their distributions or densities; multivariate distributions; mathematical expectation; special distributions and densities.

**MAT 382
TOPICS IN MATHEMATICAL STATISTICS
3, 3/0**

*Prerequisites: MAT 263, MAT 381.*

Sampling distributions; central-limit theorem; point and interval estimation; tests of hypotheses.

**MAT 383
APPLIED STATISTICS
3, 2/1**

*Prerequisites: MAT 382 or MAT 325 or MAT 311; MAT 381.*

Categorical data analysis; simple linear regression and correlation; multiple linear regression; experimental design models (one, two, or more factors); nonparametric statistics.

**MAT 390
INTRODUCTION TO OPERATIONS RESEARCH
3, 3/0**

*Prerequisites: MAT 202, MAT 270.*

Optimization of real-world problems modeled by linear objective functions subject to systems of linear inequalities and solved by either the two-phase revised simplex method or the network simplex method. Mathematics behind these methods. Applications in such diverse areas as business management, industry, economics, finance, game theory, geometry, and networks.

**MAT 401
INTRODUCTION TO COMPUTABILITY
3, 3/0**

*Prerequisites: MAT 270; MAT 301 or MAT 351.*

Introduction to topics in finite automata and Turing machines, including universal Turing machines and abstract computability.

**MAT 404
APPLICATIONS OF LINEAR ALGEBRA
3, 3/0**

*Prerequisites: MAT 202, MAT 263, and MAT 264. *

Eigenvalue problems; diagonalizing matrices; linear programming; simplex method; applications to areas such as business, industry, economics, social sciences, and behavioral sciences. Offered fall only.

**MAT 411****COMPLEX VARIABLES
3, 3/0**

*Prerequisite: MAT 263.*

Complex numbers; analytic functions; elementary functions; contour integration; integral theorems; Taylor series; Laurent series; uniform convergence; calculus of residues; mappings and applications.

**MAT 417
INTRODUCTION TO REAL ANALYSIS I
3, 3/0**

*Prerequisite: MAT 263.*

Elementary real analysis, including properties and axioms of the real number system; relations and functions; sequences; continuity; differentiation; infinite series; power series; Riemann integral.

**MAT 418
INTRODUCTION TO REAL ANALYSIS II
3, 3/0**

*Prerequisite: MAT 417 or equivalent.*

Continuation of MAT 417 with topics chosen from Riemann-Stieltjes integration, improper integrals, infinite series, series of functions, partial differentiation, Jacobians, implicit function, multiple integrals, Fubini’s Theorem.

**MAT 431
MATHEMATICAL LOGIC
3, 3/0**

*Prerequisites: MAT 270, MAT 202.*

Validity, deductibility, and completeness in propositional and predicate logics; first-order formal theories and informal theories in the context of set theory.

**MAT 461
NUMERICAL ANALYSIS
3, 3/0**

*Prerequisites: MAT 202, MAT 263, MAT 264.*

Numerical solutions (and error analysis) to linear and nonlinear equations; interpolation; curve fitting; function approximation; numerical differentiation and integration; differential equations.

**MAT 471
INTRODUCTION TO TOPOLOGY
3, 3/0**

*Prerequisites: MAT 270; MAT 301 or MAT 417.*

Introduction to topology: sets and functions; metric spaces; topological spaces; connectedness; compactness; separation.

**MAT 490
SEMINAR
3, 3/0**

*Prerequisite: Senior mathematics major or permission of instructor.*

Investigation of topics of current interest to mathematicians, such as group theory; game theory; differential geometry; measure theory; sampling theory. Emphasis on oral presentations and discussions.

**MAT 491
CAPSTONE RESEARCH IN MATHEMATICS
3, 3/0**

*Prerequisites: MAT 301 or MAT 417, senior status or permission of instructor.*

Independent research under the direction of the instructor. Composition of a research paper and presentation of results at a seminar for faculty and students.

Buffalo, NY 14222 • Phone: (716) 878-5621 • Fax: (716) 878-6107

brusehm@buffalostate.edu

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