MAT 100

Precalculus/Prestatistics

Professor/Instructor

Jennifer Michelle Johnson

An intensive and rigorous treatment of algebra and trigonometry as preparation for further courses in calculus or statistics. Topics include functions and their graphs, equations involving polynomial and rational functions, exponentials, logarithms and trigonometry.

MAT 102

Survey of Calculus

Professor/Instructor

One semester survey of the major concepts and computational techniques of calculus including limits, derivatives and integrals. Emphasis on basic examples and applications of calculus including approximation, differential equations, rates of change and error estimation for students who will take no further calculus. Prerequisites: MAT100 or equivalent. Restrictions: Cannot receive course credit for both MAT103 and MAT102. Provides adequate preparation for MAT175. Three classes.

MAT 103

Calculus I

Professor/Instructor

First semester of calculus. Topics include limits, continuity, the derivative, basic differentiation formulas and applications (curve-sketching, optimization, related rates), definite and indefinite integrals, the fundamental theorem of calculus. The fall offering will emphasize applications to physics and engineering in preparation for MAT104; the spring offering will emphasize applications to economics and life sciences, in preparation for MAT175. Prerequisite: MAT100 or equivalent. Three classes.

MAT 104

Calculus II

Professor/Instructor

Continuation of MAT103. Topics include techniques of integration, arclength, area, volume, convergence of series and improper integrals, L'Hopital's rule, power series and Taylor's theorem, introduction to differential equations and complex numbers. Prerequisite: MAT103 or equivalent. Three classes.

MAT 175

Mathematics for Economics/Life Sciences

Professor/Instructor

Survey of topics from multivariable calculus as preparation for future course work in economics or life sciences. Topics include basic techniques of integration, average value, vectors, partial derivatives, gradient, optimization of multivariable functions, and constrained optimization with Lagrange multipliers. Students preparing for math track econometrics and finance courses need MAT201/202 instead. Students who complete 175 can continue in 202 if they wish.

EGR 191 / MAT 191 / PHY 191

An Integrated Introduction to Engineering, Mathematics, Physics

Professor/Instructor

Daniel Robert Marlow

Taken concurrently with EGR/MAT/PHY 192. An integrated course that covers the material of PHY 103 and MAT 201 with the emphasis on applications to engineering. Physics topics include: mechanics with applications to fluid mechanics, wave phenomena, and thermodynamics. The lab revolves around a single project to build, launch, and analyze the flight dynamics of water-propelled rockets. One lecture, three preceptorials, one three-hour laboratory.

EGR 192 / MAT 192 / PHY 192 / APC 192

An Integrated Introduction to Engineering, Mathematics, Physics

Professor/Instructor

Christine Jiayou Taylor

Taken concurrently with EGR/MAT/PHY 191. An integrated course that covers the material of PHY 103 and MAT 201 with the emphasis on applications to engineering. Math topics include: vector calculus; partial derivatives and matrices; line integrals; simple differential equations; surface and volume integrals; and Green's, Stokes's, and divergence theorems. One lecture, two preceptorials.

APC 199 / MAT 199

Math Alive

Professor/Instructor

An exploration of some of the mathematical ideas behind important modern applications, from banking and computing to listening to music. Intended for students who have not had college-level mathematics and are not planning to major in a mathematically based field. The course is organized in independent two-week modules focusing on particular applications, such as bar codes, CD-players, population models, and space flight. The emphasis is on ideas and mathematical reasoning, not on sophisticated mathematical techniques. Two 90-minute classes, one computer laboratory.

MAT 201

Multivariable Calculus

Professor/Instructor

Vectors in the plane and in space, vector functions and motion, surfaces, coordinate systems, functions of two or three variables and their derivatives, maxima and minima and applications, double and triple integrals, vector fields, and Stokes's theorem. Prerequisite: 104 or equivalent. Three classes.

MAT 202

Linear Algebra with Applications

Professor/Instructor

Companion course to MAT201. Matrices, linear transformations, linear independence and dimension, bases and coordinates, determinants, orthogonal projection, least squares, eigenvectors and their applications to quadratic forms and dynamical systems.Three classes.

MAT 203

Advanced Vector Calculus

Professor/Instructor

Hansheng Diao

Vector spaces, limits, derivatives of vector-valued functions, Taylor's formula, Lagrange multipliers, double and triple integrals, change of coordinates, surface and line integrals, generalizations of the fundamental theorem of calculus to higher dimensions. More abstract than 201 but more concrete than 218. Recommended for prospective physics majors and others with a strong interest in applied mathematics. Prerequisite: MAT104 or MAT215 or equivalent. Three classes.

MAT 204

Advanced Linear Algebra with Applications

Professor/Instructor

Christine Jiayou Taylor

Companion course to MAT203. Linear systems of equations, linear independence and dimension, linear transforms, determinants, (real and complex) eigenvectors and eigenvalues, orthogonality, spectral theorem, singular value decomposition, Jordan forms, other topics as time permits. More abstract than MAT202 but more concrete than MAT217. Recommended for prospective physics majors and others with a strong interest in applied mathematics. Prerequisite: MAT104 or MAT215 or equivalent. Three classes.

MAT 214

Numbers, Equations, and Proofs

Professor/Instructor

Ziyang Gao

An introduction to classical number theory to prepare for higher-level courses in the department. Topics include Pythagorean triples and sums of squares, unique factorization, Chinese remainder theorem, arithmetic of Gaussian integers, finite fields and cryptography, arithmetic functions, and quadratic reciprocity. There will be a topic from more advanced or more applied number theory such as p-adic numbers, cryptography, and Fermat's Last Theorem. This course is suitable both for students preparing to enter the mathematics department and for non-majors interested in exposure to higher mathematics.

MAT 215

Honors Analysis (Single Variable)

Professor/Instructor

Charles Louis Fefferman, John Vincent Pardon

An introduction to the mathematical discipline of analysis, to prepare for higher-level course work in the department. Topics include the rigorous epsilon-delta treatment of limits, convergence, and uniform convergence of sequences and series. Continuity, uniform continuity, and differentiability of functions. The Heine-Borel theorem, the Riemann integral, conditions for integrability of functions and term by term differentiation and integration of series of functions, Taylor's theorem.

MAT 217

Honors Linear Algebra

Professor/Instructor

A rigorous course in linear algebra with an emphasis on proof rather than applications. Topics include vector spaces, linear transformations, inner product spaces, determinants, eigenvalues, the Cayley-Hamilton theorem, Jordan form, the spectral theorem for normal transformations, bilinear and quadratic forms.

MAT 218

Accelerated Honors Analysis II

Professor/Instructor

Robert Clifford Gunning

Continuation of MAT216, Accelerated Analysis I from the fall. A rigorous course in analysis with an emphasis on proof rather than applications. Topics include metric spaces, completeness, compactness, total derivatives, partial derivatives, inverse function theorem, implicit function theorem, Riemann integrals in several variables, Fubini. See the department website for details: http://www.math.princeton.edu.

MAT 305

Mathematical Logic

Professor/Instructor

A development of logic from the mathematical viewpoint, including propositional and predicate calculus, consequence and deduction, truth and satisfaction, the Goedel completeness and incompleteness theorems. Applications to model theory, recursion theory, and set theory as time permits. Some underclass background in logic or in mathematics is recommended.

PHI 323 / MAT 306

Advanced Logic

Professor/Instructor

John P. Burgess

This course deals with topics chosen from recursion theory, proof theory, and model theory. In recent years the course has most often given an introduction to recursion theory with applications to formal systems. Two 90-minute classes. Prerequisite: 312 or instructor's permission.

MAT 320

Introduction to Real Analysis

Professor/Instructor

Mihaela I. Ignatova

Introduction to real analysis, including the theory of Lebesgue measure and integration on the line and n-dimensional space and the theory of Fourier series. Prerequisite: MAT201 and MAT202 or equivalent.

MAT 323 / APC 323

Topics in Mathematical Modeling

Professor/Instructor

Zahra Aminzare

Draws problems from the sciences & engineering for which mathematical models have been developed and analyzed to describe, understand and predict natural and man-made phenomena. Emphasizes model building strategies, analytical and computational methods, and how scientific problems motivate new mathematics. This interdisciplinary course in collaboration with Molecular Biology, Psychology and the Program in Neuroscience is directed toward upper class undergraduate students and first-year graduate students with knowledge of linear algebra and differential equations.

MAT 325

Analysis I: Fourier Series and Partial Differential Equations

Professor/Instructor

Alexandru D. Ionescu

Basic facts about Fourier Series, Fourier Transformations, and applications to the classical partial differential equations will be covered. Also Fast Fourier Transforms, Finite Fourier Series, Dirichlet Characters, and applications to properties of primes. Prerequisites: 215, 218, or permission of instructor.

MAT 330

Complex Analysis with Applications

Professor/Instructor

Michael Aizenman

The theory of functions of one complex variable, covering power series expansions, residues, contour integration, and conformal mapping. Although the theory will be given adequate treatment, the emphasis of this course is the use of complex analysis as a tool for solving problems. Prerequisite: MAT201 and MAT202 or equivalent.

MAT 335

Analysis II: Complex Analysis

Professor/Instructor

Elias M. Stein

Study of functions of a complex variable, with emphasis on interrelations with other parts of mathematics. Cauchy's theorems, singularities, contour integration, power series, infinite products. The gamma and zeta functions and the prime number theorem. Elliptic functions, theta functions, Jacobi's triple product and combinatorics. An overall view of Special Functions via the hypergeometric series. This course is the second semester of a four-semester sequence, but may be taken independently of the other semesters.

MAT 345

Algebra I

Professor/Instructor

Nicholas Michael Katz

This course will be devoted to Galois theory, developing the necessary group theory (including the Sylow theorems) and algebra from scratch.

MAT 346

Algebra II

Professor/Instructor

Continuation of MAT345. Further develop knowledge of algebraic structures by exploring examples that connect to higher mathematics. There will be opportunities for a student to explore an advanced topic in great depth, possibly for a junior project.