Undergraduate Bulletin

Spring 2024

MAT: Mathematics

MAT 118: Mathematical Thinking

Development of quantitative thinking and problem solving abilities through a selection of mathematical topics: logic and reasoning; numbers, functions, and modeling; combinatorics and probability; growth and change. Other topics may include geometry, statistics, game theory, and graph theory. Through their engagement in problem solving, students develop an appreciation of the intellectual scope of mathematics and its connections with other disciplines.

Prerequisite: C or better in MAP 103 or level 2+ or higher on the mathematics placement examination

(Prerequisite must be met within one year of beginning this course.)

DEC:     C
SBC:     QPS

3 credits

MAT 119: Foundations for Precalculus

This course is a companion to MAT 123: Precalculus, providing a structured environment where students can refresh the algebra skills which are necessary for success in precalculus. These topics include understanding of exponents (especially fractional and negative exponents), manipulating mathemematical expressions, solving equations, and modeling/word problems. Course may not be taken with CHE 129.

Prerequisite: 2+ on placement or permission of MAT 123 instructor

Corequisite: MAT 123

1 credit, S/U grading

MAT 122: Overview of Calculus with Applications

The basics of calculus in a self-contained, one-semester course. Properties and applications of polynomial, exponential, and logarithmic functions. Derivatives: slopes, rates of change, optimization, integrals, area, cumulative change, and average. The fundamental theorem of calculus. Emphasis on modeling examples from economics. Students who subsequently wish to enroll in MAT 125 or 131 will be required to score level 4 on the mathematics placement examination before taking either course. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or better in MAP 103 or level 3 on the mathematics placement exam

(Prerequisite must be met within one year prior to beginning the course.)

DEC:     C
SBC:     QPS

3 credits

MAT 123: Precalculus

Comprehensive preparation for the regular calculus sequences. Careful development of rational, exponential, logarithmic, and trigonometric functions, and their applications. Asymptotics and curve sketching. General modeling examples. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or better in MAP 103 or level 3 on the mathematics placement exam or corequisite MAT 119 (Prerequisite must be met within one year prior to beginning the course.)

DEC:     C
SBC:     QPS

3 credits

MAT 125: Calculus A

Differential calculus, emphasizing conceptual understanding, computations and applications, for students who have the necessary background from 12th-year high school mathematics. Limits and continuous functions. Differentiation of elementary algebraic, trigonometric, exponential and logarithmic functions; graphing; modeling; and maximization. L'Hospital's rule. May not be taken for credit in addition to MAT 131 or 141 or AMS 151. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or higher in MAT 123; or level 4 on the mathematics placement examination; or corequisite MAT 130

DEC:     C
SBC:     QPS

3 credits

MAT 126: Calculus B

A continuation of MAT 125, covering integral calculus: Riemann sums, the fundamental theorem, symbolic and numeric methods of integration, area under a curve, volume, applications such as work and probability, improper integrals. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or higher in MAT 125 or 131 or 141 or AMS 151 or level 6 on the mathematics placement examination

DEC:     C
SBC:     QPS

3 credits

MAT 127: Calculus C

A continuation of MAT 126, covering: sequences, series, Taylor series, differential equations and modeling. May not be taken for credit in addition to MAT 132, MAT 142, MAT 171, or AMS 161. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or higher in MAT 126 or level 8 on the mathematics placement examination

DEC:     C
SBC:     QPS

3 credits

MAT 130: Trigonometry and Logarithms

Inverse functions, exponential and logarithmic functions, radian measure of angles and trigonometric functions. Taught as a companion to MAT 125.

Prerequisite: MAT 122 with a grade of C or better, or level 3+ or higher on the placement exam, or permission of instructor

Co-requisite: MAT 125

1 credit, S/U grading

MAT 131: Calculus I

The differential calculus and integral calculus, emphasizing conceptual understanding, computations and applications, for students who have the necessary background from 12th-year high school mathematics. Differentiation of elementary algebraic; trigonometric, exponential, and logarithmic functions; graphing; modelling and maximization; L'Hospital's rule; the Riemann integral; and the Fundamental Theorem of Calculus. May not be taken for credit in addition to MAT 125 or 141 or AMS 151. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: B or higher in MAT 123 or level 5 on the mathematics placement examination

DEC:     C
SBC:     QPS

4 credits

MAT 132: Calculus II

A continuation of MAT 131, covering symbolic and numeric methods of integration; area under a curve; volume; applications such as work and probability; sequences; series; Taylor series; differential equations; and modelling. May not be taken for credit in addition to MAT 127, MAT 142, MAT 171, or AMS 161. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or higher in AMS 151 or MAT 131 or 141, or level 7 on the mathematics placement examination

DEC:     C
SBC:     QPS

4 credits

MAT 200: Logic, Language and Proof

A basic course in the logic of mathematics, the construction of proofs and the writing of proofs. The mathematical content is primarily logic and proofs, set theory, combinatorics, functions and relations. There is considerable focus on writing. May not be taken for credit in addition to MAT 250.

Prerequisite: Level 4 on the mathematics placement examination or equivalent course or permission of the instructor

SBC:     STEM+

3 credits

MAT 203: Calculus III with Applications

Vector algebra in two and three dimensions, multivariate differential and integral calculus, optimization, vector calculus including the theorems of Green, Gauss, and Stokes. Applications to economics, engineering, and all sciences, with emphasis on numerical and graphical solutions; use of graphing calculators or computers. May not be taken for credit in addition to AMS 261.

Prerequisite: C or higher in MAT 127 or 132 or 142 or AMS 161 or level 9 on the mathematics placement examination

SBC:     STEM+

4 credits

MAT 211: Introduction to Linear Algebra

Introduction to the theory of linear algebra with some applications; vectors, vector spaces, bases and dimension, applications to geometry, linear transformations and rank, eigenvalues and eigenvectors, determinants and inner products. May not be taken for credit in addition to AMS 210.

Prerequisite: C or higher in AMS 151 or MAT 131 or 141 or coregistration in MAT 126 or level 7 on the mathematics placement examination

SBC:     STEM+

3 credits

MAT 250: Introduction to Advanced Mathematics

An introduction to the Advanced Track mathematics program. Provides the core of basic of propositional logic, quantifiers, proofs, sets, functions, cardinality, relations, equivalence relations and quotient sets, order relations, combinatorics. Number systems: natural numbers, integers, rational, real and complex numbers. MAT 250 is primarily intended for students in the Advanced Track program. It serves as an alternative to MAT 200 and may not be taken for credit in addition to MAT 200. Students wishing to enroll in MAT 250 should instead enroll in a corresponding section of MAT 200. In approximately the 3rd week, an assessment will be held and qualified students will be offered the option of moving to MAT 250. Formerly offered as MAT 150; not for credit in addition to MAT 150.

Prerequisite: MAT 131 or an equivalent course or level 7 or higher on mathematics placement examination

SBC:     QPS

4 credits

MAT 260: Problem Solving in Mathematics

Students actively solve challenging problems in plane geometry, basic number theory, and calculus, and write precise arguments. Relevant preparation for problem-solving is provided in the course.

Prerequisite: Permission of instructor

1 credit

MAT 303: Calculus IV with Applications

Homogeneous and inhomogeneous linear differential equations; systems of linear differential equations; series solutions; Laplace transforms; Fourier series. Applications to economics, engineering, and all sciences with emphasis on numerical and graphical solutions; use of computers. May not be taken for credit in addition to AMS 361 or MAT 308.

Prerequisite: C or higher in MAT 127 or 132 or 142 or AMS 161 or level 9 on the mathematics placement examination

SBC:     STEM+

4 credits

MAT 307: Multivariable Calculus with Linear Algebra

Introduction to linear algebra: vectors, matrices, systems of linear equations, bases and dimension, dot product, determinants. Multivariate differential and integral calculus, divergence and curl, line and surface integrals, theorems of Green, Gauss, and Stokes. More theoretical and intensive than MAT 203, this course is primarily intended for math majors. Together with MAT 308, it forms a 2-semester sequence covering the same material as the 3-semester sequence of MAT 203, MAT 211 and MAT 303. May not be taken for credit in addition to MAT 203 or AMS 261.

Prerequisite: MAT 127 or MAT 132

SBC:     STEM+

4 credits

MAT 308: Differential Equations with Linear Algebra

Linear algebra: determinants, eigenvalues and eigenvectors, diagonalization. Differential equations; existence and uniqueness of solutions. First- and second-order equations; linear versus nonlinear equations. Systems of linear equations. Laplace transform. Applications to physics. More theoretical and intensive than MAT 303, this course is primarily intended for math majors. Together with MAT 307, it forms a 2-semester sequence covering the same material as the 3-semester sequence of MAT 205, MAT 211 and MAT 305. May not be taken for credit in addition to MAT 303 or AMS 361.

Prerequisite: MAT 307; or MAT 203 and MAT 211; or MAT 132 and MAT 220; or permission of instructor

SBC:     STEM+

4 credits

MAT 310: Linear Algebra

Finite dimensional vector spaces, linear maps, dual spaces, bilinear functions, inner products. Additional topics such as canonical forms, multilinear algebra, numerical linear algebra.

Prerequisite: C or higher in MAT 211 or 308 or AMS 210 or MAT 220; C or higher in MAT 200 or MAT 250 or permission of instructor

4 credits

MAT 311: Number Theory

Congruences, quadratic residues, quadratic forms, continued fractions, Diophantine equations, number-theoretical functions, and properties of prime numbers.

Prerequisites: C or higher in MAT 312 or 313; C or higher in MAT 200 or MAT 250 or permission of instructor

3 credits

MAT 312: Applied Algebra

Topics in algebra: groups, informal set theory, relations, homomorphisms. Applications: error correcting codes, Burnside's theorem, computational complexity, Chinese remainder theorem. This course is offered as both AMS 351 and MAT 312.

Prerequisite: C or higher in AMS 210 or MAT 211 or MAT 220

Advisory Prerequiste: MAT 200 or CSE 215 or CSE 150 or equivalent

3 credits

MAT 313: Abstract Algebra

Groups and rings together with their homomorphisms and quotient structures. Unique factorization, polynomials, and fields.

Prerequisite: C or higher in MAT 310 or MAT 312 or MAT 315; C or higher in MAT 200 or MAT 250 or permission of instructor

3 credits

MAT 314: Abstract Algebra II

This course is a continuation of MAT 313, Abstract algebra. It covers modules over rings, including structure theorem for modules over PID, theory of fields and field extensions and introduction to Galois theory.

Prerequisite: MAT 313 or permission of the instructor

3 credits

MAT 315: Advanced Linear Algebra

Finite dimensional vector spaces over a field, linear maps, isomorphisms, dual spaces, quotient vector spaces, bilinear and quadratic functions, inner products, canonical forms of linear operators, multilinear algebra, tensors. This course serves as an alternative to MAT 310. It is an intensive course, primarily intended for math majors in Advanced Track program. Students wishing to enroll in MAT 315 should instead enroll in MAT 310. In approximately the 4th week, an assessment will be held and qualified students will be offered the option of moving to MAT 315.

Prerequisite: B or higher in MAT 200 or MAT 250; B or higher in MAT 211, AMS 219, MAT 308, or MAT 220; or permission of the instructor

4 credits

MAT 319: Foundations of Analysis

A careful study of the theory underlying topics in one-variable calculus, with an emphasis on those topics arising in high school calculus. The real number system. Limits of functions and sequences. Differentiations, integration, and the fundamental theorem. Infinite series.

Prerequisite: C or higher in MAT 200 or MAT 250 or permission of instructor; C or higher in one of the following: MAT 203, 211, 220, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161

4 credits

MAT 320: Introduction to Analysis

A careful study of the theory underlying calculus. The real number system. Basic properties of functions of one real variable. Differentiation, integration, and the inverse theorem. Infinite sequences of functions and uniform convergence. Infinite series. Metric spaces and compactness. This course is a more demanding alternative of MAT 319, suitable for students who are comfortable with rigorous proofs. Students wishing to enroll in MAT 320 should instead enroll in MAT 319. In approximately the 6th week, an assessment will be held and qualified students will be offered the option of moving to MAT 320.

Prerequisite: B or higher in MAT 200 or MAT 250 or permission of instructor; C or higher in one of the following: MAT 203, 211, 220, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161

4 credits

MAT 322: Analysis in Several Dimensions

Continuity, differentiation, and integration in Euclidean n-space. Differentiable maps. Implicit and inverse function theorems. Differential forms and the general Stokes's theorem.

Prerequisites: C or higher in MAT 203, MAT 220, MAT 307, or AMS 261; C or higher in MAT 310 or MAT 315; B or higher in MAT 320

3 credits

MAT 324: Real Analysis

Introduction to Lebesgue measure and integration. Aspects of Fourier series, function spaces, Hilbert spaces, Banach spaces.

Prerequisites: B or higher in MAT 320

3 credits

MAT 331: Computer-Assisted Mathematical Problem Solving

Exploration of the use of the computer as a tool to gain insight into complex mathematical problems through a project-oriented approach. Students learn both the relevant mathematical concepts and ways that the computer can be used (and sometimes misused) to understand them. The particular problems may vary by semester; past topics have included cryptography, fractals and recursion, modeling the flight of a glider, curve fitting, the Brachistochrone, and computer graphics. No previous experience with computers is required.

Prerequisite: C or higher in MAT 203 or 205 or 307 or AMS 261

SBC:     TECH

3 credits

MAT 336: History of Mathematics

A survey of the history of mathematics from the beginnings through the 19th century, with special attention to primary sources and to the interactions between culture and mathematics. Emphasis on topics germane to the high school curriculum. Mesopotamian, Egyptian, and Greek mathematics; non-European mathematics; early Renaissance mathematics; the birth and flowering of calculus; the beginnings of probability theory; and the origin of non-Euclidean geometries and the modern concept of number.

Prerequisite: MAT 200 or MAT 203 or or MAT 250 or MAT 307 or AMS 261

DEC:     H
SBC:     SPK, STAS, WRTD

3 credits

MAT 341: Applied Real Analysis

Partial differential equations of mathematical physics: the heat, wave, and Laplace equations. Solutions by techniques such as separation of variables using orthogonal functions (e.g., Fourier series, Bessel functions, Legendre polynomials). D'Alembert solution of the wave equation.

Prerequisites: C or higher in the following: MAT 203 or 220 or 307 or AMS 261; MAT 303 or 305 or 308 or AMS 361

Advisory Prerequisite: MAT 200 or MAT 250

3 credits

MAT 342: Applied Complex Analysis

Complex numbers, analytic functions, the Cauchy-Riemann and Laplace equations, the Cauchy integral formula and applications. Fundamental Theorem of Algebra and the Maximum Principle. The Cauchy residue theorem and applications to evaluating real integrals. Conformal mappings.

Prerequisite: C or higher in the following: MAT 203 or MAT 220 or MAT 307 or AMS 261

Advisory Prerequisite: MAT 200 or MAT 250

3 credits

MAT 351: Differential Equations: Dynamics and Chaos

A study of the long-term behavior of solutions to ordinary differential equations or of iterated mappings, emphasizing the distinction between stability on the one hand and sensitive dependence and chaotic behavior on the other. The course describes examples of chaotic behavior and of fractal attractors, and develops some mathematical tools for understanding them.

Prerequisites: C or higher in the following: MAT 203 or MAT 220 or MAT 307 or AMS 261; MAT 303 or MAT 308 or AMS 361; MAT 200 or MAT 250 or permission of instructor

3 credits

MAT 360: Geometric Structures

Formal geometries and models. Topics selected from projective, affine, Euclidean, and non-Euclidean geometries.

Pre- or Corequisites: MAT 203 or 220 or 307 or AMS 261; MAT 200 or MAT 250 or permission of instructor

3 credits

MAT 362: Differential Geometry of Surfaces

The local and global geometry of surfaces: geodesics, parallel transport, curvature, isometries, the Gauss map, the Gauss-Bonnet theorem.

Prerequisite: C or higher in MAT 319 or MAT 320 or MAT 364; MAT 203 or MAT 307 or MAT 322

3 credits

MAT 364: Topology and Geometry

A broadly based introduction to topology and geometry, the mathematical theories of shape, form, and rigid structure. Topics include intuitive knot theory, lattices and tilings, non-Euclidean geometry, smooth curves and surfaces in Euclidean 3-space, open sets and continuity, combinatorial and algebraic invariants of spaces, higher dimensional spaces.

Prerequisites: MAT 203 or 220 or 307 or AMS 261; MAT 200 or 250

Advisory Prerequisite: MAT 319 or 320

3 credits

MAT 371: Logic

A survey of the logical foundations of mathematics: development of propositional calculus and quantification theory, the notions of a proof and of a model, the completeness theorem, Goedel's incompleteness theorem. This course is offered as both CSE 371 and MAT 371.

Prerequisite: CSE 150 or CSE 215 or MAT 200 or MAT 250

3 credits

MAT 373: Analysis of Algorithms

Mathematical analysis of a variety of computer algorithms including searching, sorting, matrix multiplication, fast Fourier transform, and graph algorithms. Time and space complexity. Upper-bound, lower- bound, and average-case analysis. Introduction to NP completeness. Some machine computation is required for the implementation and comparison of algorithms. This course is offered as CSE 373 and MAT 373. Not for credit in addition to CSE 385.

Prerequisites: C or higher in: CSE 150 or CSE 215 or MAT 200 or MAT 250; MAT 211 or AMS 210; CSE 214 or CSE 260; CSE or MAT major

3 credits

MAT 401: Seminar in Mathematics

Discussions of a specific area of interest in mathematics. The work of each semester covers a different area of mathematics. May be repeated as topic changes. Prerequisites will be announced with the topic each time the course is offered.

Prerequisite: U3/U4; permission of department or instructor; additional prerequisites announced with topic

SBC:     SPK

3 credits

MAT 402: Seminar in Mathematics

Discussions of a specific area of interest in mathematics. The work of each semester covers a different area of mathematics. May be repeated as topic changes. Prerequisites will be announced with the topic each time the course is offered.

Prerequisite: U3/U4; permission of department or instructor; additional prerequisites announced with topic

SBC:     SPK

3 credits

MAT 444: Experiential Learning

This course is designed for students who engage in a substantial, structured experiential learning activity in conjunction with another class. Experiential learning occurs when knowledge acquired through formal learning and past experience are applied to a "real-world" setting or problem to create new knowledge through a process of reflection, critical analysis, feedback and synthesis. Beyond-the-classroom experiences that support experiential learning may include: service learning, mentored research, field work, or an internship.

Prerequisite: WRT 102 or equivalent; permission of the instructor and approval of the EXP+ contract (http://sb.cc.stonybrook.edu/bulletin/current/policiesandregulations/degree_requirements/EXPplus.php)

SBC:     EXP+

0 credit, S/U grading

MAT 458: Speak Effectively Before an Audience

A zero credit course that may be taken in conjunction with any MAT course that provides opportunity to achieve the learning outcomes of the Stony Brook Curriculum's SPK learning objective.

Pre- or corequisite: WRT 102 or equivalent; permission of the instructor

SBC:     SPK

0 credit, S/U grading

MAT 459: Write Effectively in Mathematics

A zero credit course that may be taken in conjunction with any 300- or 400-level MAT course, with permission of the instructor. The course provides opportunity to practice the skills and techniques of effective academic writing and satisfies the learning outcomes of the Stony Brook Curriculum's WRTD learning objective.

Prerequisite: WRT 102; permission of the instructor

SBC:     WRTD

0 credit, S/U grading

MAT 475: Undergraduate Teaching Practicum

Each student assists in teaching a lower-division mathematics course or works in the Mathematics Learning Center. The student's work is regularly supervised by a faculty member. In addition, a weekly seminar is conducted. Responsibilities may include preparation of materials for student use and discussions, helping students with problems, and involvement in "alternative" teaching projects. Intended for upper-division students who have excelled in the calculus sequence. May not be used for major credit.

Prerequisite: Permission of the director of undergraduate studies

SBC:     EXP+

3 credits, S/U grading

MAT 487: Independent Study in Special Topics

A reading course for juniors and seniors. The topics may be chosen by the student with the approval of a supervising member of the faculty, who also takes responsibility for evaluation. A topic that is covered in a course regularly offered by the department is not appropriate for independent study. May be repeated.

Prerequisite: Permission of the director of undergraduate studies

0-6 credits

MAT 495: Honors Thesis

The student and a supervising faculty member together choose a topic in mathematics, and the student writes a substantial paper expounding the topic in a new way.

Prerequisite: Permission of the director of undergraduate studies

SBC:     EXP+, WRTD

3 credits