# MATH - Mathematics

## MATH 100 Mathematics First-Year Seminar

The course seeks to help students utilize campus resources effectively, learn useful academic skills, especially those relevant to mathematics, develop a support network, become more self-aware, promote personal health and wellness, and better connect with the campus. The course will introduce students to the culture of the Mathematical Sciences department and the mathematics community in general. Students in the course should be concurrently enrolled in a precalculus or calculus course.

## MATH 105 Precalculus

The course is designed to prepare students to take Survey of Calculus I (MATH 120) or University Calculus I (MATH 122). It emphasizes multi-step problem solving. Topics include algebraic, exponential, logarithmic, and trigonometric functions and their graphs, transformations and combinations of functions, a review of algebra, geometry, and trigonometry, solving inequalities and systems of equations, and computational technology. (The course is not open to students who have completed MATH 106 with a grade of C- or better, or those who have completed a calculus course.) Background assumed: N.Y.S. Integrated Algebra and Trigonometry, or equivalent.

## MATH 106 University Precalculus

The course is designed to prepare students to take University Calculus (MATH 122) and emphasizes multi-step problem solving. Topics include a review of algebra, solving inequalities, algebraic and transcendental functions, trigonometry, analytic geometry, applications and computational technology. (Not open to students who have completed a calculus course with a grade of C- or better.) Background assumed: N.Y.S. Algebra II and Trigonometry (or Math B), or equivalent.

## MATH 108 Prize-Winning Mathematics

The course surveys some mathematical tools that have proved useful to the social sciences, especially in business, economics, and political science. Work on one topic in particular, game theory, has led to several Nobel prizes, and may have helped the New England Patriots win three Super Bowls. Other topics will be selected from linear models, matrices, linear programming, and nonlinear and probabilistic models. Background assumed: N.Y.S. Algebra II and Trigonometry (or Math B), or equivalent.

## MATH 110 Mathematics in Action

Emphasizes the real-world significance of mathematics and the applications of several areas of mathematics. Some topics: design of street networks, planning and scheduling, weighted voting systems, fair division and apportionment, measuring populations and the universe, and statistics. Background assumed: N.Y.S. Algebra II and Trigonometry (or Math B), or equivalent.

## MATH 112 Preparation for Calculus

Designed for students who plan to take first-semester calculus in the following semester, and want to hone their precalculus skills. The course utilizes an online system called ALEKS (Assessment and LEarning in Knowledge Spaces), an artificially-intelligent assessment and learning system. ALEKS uses adaptive questioning to determine exactly what each student knows, and then tailors a study plan to each individual student. Students work at their own pace to attain mastery of the prerequisite knowledge necessary for success in calculus. Not open to students with credit for calculus.

## MATH 117 Why Mathematics?

Introduces the liberal arts student to the nature of mathematics and what mathematicians do. An emphasis on presenting ideas and mathematical concepts rather than on attaining computational skills. Ideas from algebra, geometry, number theory, set theory and topology are presented with emphasis on their history and relevance to other disciplines. Background assumed: N.Y.S. Algebra II and Trigonometry (or Math B), or equivalent.

## MATH 120 Survey of Calculus I

An introduction to differential and integral calculus for functions of a single variable with applications to the management, social, and life sciences. Not open to students majoring in mathematics, physics, or chemistry. Background assumed: Preparation equivalent to MATH 105 or MATH 106. Credit may not be earned for both MATH 120 and MATH 122.

## MATH 121 Survey of Calculus II

A continuation of MATH 120. Additional techniques of differentiation and integration with further applications to the management, social, and life sciences. Introduction to the calculus of functions of several variables. Not open to students majoring in mathematics, physics, or chemistry. Credit may not be earned for both MATH 121 and MATH 123.

### Prerequisites

MATH 120## MATH 122 University Calculus I

Functions, inverse functions, limits, continuity, derivatives, indeterminate forms, antiderivatives; applications to rectilinear motion, graphing, maxima-minima, related rates; computational technology. Background assumed: Preparation equivalent to MATH 105 or MATH 106. Credit will not be given for both MATH 120 and MATH 122.

## MATH 123 University Calculus II

Definite integrals, the fundamental theorem of calculus, techniques of integration, applications of the definite integral in the physical sciences and geometry, improper integrals, differential equations, sequences and series. Credit will not be given for both MATH 121 and MATH 123.

### Prerequisites

MATH 122## MATH 125 Software for Mathematics

Introduction to software packages used by mathematicians. Topics selected from: computer algebra systems, spreadsheet software, and software for publishing mathematics (both in print and on the Web). Some attention is given to writing programs and macros within these systems.

### Prerequisites

MATH 122## MATH 190 Honors Problem Solving

Designed to engage promising mathematics students in solving problems related to calculus and its applications. Students are partitioned into small groups and given interesting and nontrivial problems to work on together. Students present solutions in class and are required to record their work in notebooks.

### Corequisites

MATH 123## MATH 201 Concepts of Foundational Mathematics: A Problem Solving Approach

The course explores the foundational concepts of modern mathematics. A problem solving approach is incorporated to discover fundamental structure and meaning associated with central content themes of Number Systems, Functions/Patterns, Statistics/Probability, Geometry, and Measurement. Prerequisite: Sophomore standing

## MATH 210 Mathematical Structures and Proof

Careful study of the concepts and techniques often used in mathematics courses at the advanced undergraduate level. Topics include logic, set theory, proof techniques, elementary number theory, mathematical induction, functions, and relations. Additional topics from abstract algebra, combinatorics, or countable vs. uncountable sets as time permits.

### Prerequisites

MATH 121 or MATH 123## MATH 223 University Calculus III

Parametric equations, polar, cylindrical, and spherical coordinates, algebra of vectors, equations of lines, planes, quadratic surfaces, vector functions and space curves, calculus of functions of several variables including multiple integration; applications to the physical sciences and geometry; computational technology.

### Prerequisites

MATH 123## MATH 224 Differential Equations

Introductory course with emphasis on methods of solution of differential equations and applications. Topics include: first order differential equations, higher order linear differential equations, method of undetermined coefficients, method of variation of parameters, systems of first order linear differential equations, qualitative and numerical analyses of solutions, and power series solutions and Laplace transforms as time permits.

### Prerequisites

MATH 123## MATH 231 Linear Algebra

Careful study of matrices, systems of linear equations, determinants, linear transformations, with emphasis on similarities and isometries of the plane, vector spaces, eigenvalues and eigenvectors; other topics as time permits. Completion of, or concurrent enrollment in MATH 210 is recommended.

### Prerequisites

MATH 121 or MATH 123## MATH 290 Sophomore Honors Mathematics

Mathematics majors who excel in calculus and/or discrete mathematics may be invited to join the Honors Program in Mathematics. MATH 290 is the first course in the Honors Program. It looks at advanced topics from calculus, discrete mathematics, and linear algebra, with emphasis on reading and writing mathematical proofs.

### Prerequisites

MATH 210### Corequisites

MATH 231## MATH 307 Math and Music

Explores how mathematical ideas have been used to understand and create music, and how musical ideas have influenced math and science. Topics selected from the history of tuning and alternative tuning, the Music of the Spheres doctrine, historical theories of consonance, contributions to music theory by mathematicians, mathematical analysis of sound, philosophical and cognitive connections between math and music, and math in music composition and instrument design. An ability to read music is recommended. This course is not intended for Mathematics majors.

## MATH 309 Mathematical Sciences Internship

Participation in an approved professional experience applying mathematics or statistics in a real world setting. Students must submit a Learning Contract describing the work experience, its relationship to the mathematical sciences, and how it will be monitored and evaluated. Permission of the department required.

## MATH 315 Theory of Equations

Study of the theory of polynomial equations. Rational, real and complex roots of algebraic equations, the Remainder and Factor theorems, Fundamental Theorem of Algebra, solutions of cubic and bi-quadratic equations and approximation of roots.

### Prerequisites

MATH 210## MATH 322 Partial Differential Equations

Introductory course in partial differential equations with emphasis on boundary value problems encountered in mathematical physics. Fourier series; separation of variables; D'Alembert's solution; the heat, wave and potential equations. Additional topics such as Sturm-Liouville problems or Laplace transforms as time permits.

### Prerequisites

MATH 224## MATH 323 Introductory Real Analysis

Careful presentation of the ideas of calculus that are developed intuitively in the usual freshman-sophomore calculus courses. Techniques of proof in analysis; countable sets and cardinality; the real line as a complete ordered field; some topology of the real line; sequences and their limits; continuous functions and their properties; other topics as time permits.

### Prerequisites

MATH 123 and MATH 210## MATH 325 Numerical Analysis

Introductory course in numerical methods for digital computers. Floating point arithmetic, errors, error analysis. Roots of equations, systems of equations. Numerical differentiation and integration. Interpolation and least squares approximations.

### Prerequisites

MATH 123## MATH 329 Mathematical Modeling

An introduction to the development of mathematical models to solve various applied and industrial problems. Topics will include optimization, Lagrange multipliers, sensitivity analysis in optimization models, analysis and simulation of discrete and continuous dynamic models.

### Prerequisites

MATH 223 and MATH 231## MATH 331 Abstract Algebra I

Study of algebraic structures, such as groups and rings. The fundamental theorem of finite abelian groups, basic homomorphism theorems for groups, permutation groups and polynomial rings are presented.

### Prerequisites

MATH 210 and MATH 231## MATH 332 Abstract Algebra II

Continuation of the study of algebraic structures such as groups, rings, integral domains and fields, with applications such as: geometric symmetry and crystallography, switching networks, and error-correcting codes.

### Prerequisites

MATH 331## MATH 335 Number Theory

Study of integers and their properties; divisibility; primes; congruencies; multiplicative functions; quadratic residues; quadratic reciprocity; Diophantine equations.

### Prerequisites

MATH 210## MATH 337 Combinatorics

The addition, multiplication and pigeon-hole principles. Permutations and combinations, partitions and distributions; the binomial and multinomial theorems. Generating functions; recurrence relations; principle of inclusion-exclusion; combinatorial algorithms or designs as time permits.

### Prerequisites

MATH 210 and MATH 231## MATH 341 Geometry

Study of absolute, Euclidean, and hyperbolic geometry from synthetic and analytic viewpoints. Topics include axioms for geometries, transformations, triangles and other basic shapes, and constructions. Some consideration given to finite, spherical, and spatial geometry. Use of geometry software.

### Prerequisites

MATH 210## MATH 359 Probability Models in Operations Research

Topics chosen from stochastic processes; birth-death processes; queuing theory; inventory theory; reliability; decision analysis; simulation.

### Prerequisites

STAT 350 and MATH 231## MATH 365 Financial Mathematics

Study of basic financial mathematical concepts used in modeling and hedging. Topics include: financial derivatives, call and put options, futures, binomial trees, replicating portfolios and arbitrage, stocks and options pricing, Black-Scholes model, hedging. Additional topics such as swaps, currency markets, and international political risk analysis as time permits.

### Prerequisites

MATH 231 and STAT 350## MATH 369 Interest Theory

A rigorous treatment of the mathematical theory associated with financial transactions, including simple and compound interest, annuities, bonds, yield rates, amortization schedules, and sinking funds. Additional topics such as capital asset pricing models and portfolio risk analysis as time permits.

### Prerequisites

MATH 123## MATH 375 Deterministic Models in Operations Research

Topics chosen from linear programming and applications; network analysis; game theory; dynamic, integer and nonlinear programming.

### Prerequisites

MATH 231## MATH 381 History of Mathematics

Chronological study of the development of mathematics. Emphasis on the solution of selected mathematical problems associated with historical periods.

### Prerequisites

MATH 210## MATH 390 Honors Special Topics

The course, the second in the Honors Program in Mathematics, will focus on a topic reflecting the interest of the instructor. Examples include combinatorial topology, nonlinear dynamic systems, graph theory, complex analysis, and the theory of partitions. This course is by invitation only.

### Prerequisites

MATH 290## MATH 400 Independent Study

Independent study of a selected list of readings approved by a faculty advisor. Permission of department required.

## MATH 405 Senior Seminar

Studies from selected areas of mathematics. Written reports and formal presentations will be required. Senior standing or permission of instructor required.

## MATH 406 Applied Math Senior Seminar

Students are partitioned into small groups and given problems from the Mathematical Contest in Modeling, or similar material, to work on together. Written reports and formal presentations will be required. Departmental approval required.

## MATH 408 Special Topics Seminar

Selected readings, discussions, and reports on topics in mathematics. Permission of department required.

## MATH 420 Advanced Calculus

Vector calculus; Jacobian matrices and their determinants; differentiation and integration of differential forms and applications to physics; generalizations of the fundamental theorem of calculus, including Green's theorem, the divergence theorem, Gauss's theorem, and Stokes' theorem; potential theory.

### Prerequisites

MATH 231 and MATH 223## MATH 423 Topics in Analysis

Topics vary, depending on the instructor, but may include measure and integration, basic functional analysis, complex analysis, residue theory, and special functions.

### Prerequisites

MATH 323## MATH 440 Graph Theory

Introduction to graph theory. Topics chosen from: connectivity, trees, eulerian and hamiltonian graphs, matchings, factorizations, and colorings. Applications chosen from: the shortest path problem, communication networks, the traveling salesman problem, the optimal assignment problem, and scheduling algorithms.

### Prerequisites

MATH 210 and MATH 231## MATH 490 Honors Thesis

The capstone course in the Honors Program in Mathematics. Each student will conduct research under the mentorship of a faculty member, culminating in a written thesis and an oral presentation. This course is by invitation only.