# Undergraduate Mathematics Courses

**MATH 119: Elements of Calculus, Part I**

Another option for students who have not studied calculus before. This course is linked to Math 120, and students must complete both courses to receive credit for Math 119. There is an emphasis on applications to biology, economics and physics. After completing the sequence, students may continue in Math 122.

**MATH 120: Elements of Calculus, Part II**

The linked sequence continuation of Math 119.

**MATH 121: Calculus I, Part I**

Calculus for students who have had calculus before, but need a refresher, or for mathematically adept students who have not had calculus before. More theoretical and also more algebraicially demanding than Math 117, this is the recommended introductory calculus course for prospective math and science majors. This is probably the one to take for pre-med or pre-law as well. Topics include limits, continuity, derivatives, related rates, maxima and minima, graphing, and integration. Advanced placement credit is given for this course for students with a 4 or a 5 on either AP calculus exam.

**MATH 122: Calculus I, Part II **

The continuation of Math 121, knowledge of which is a prerequisite for this course. Integration and applications thereof, techniques of integration, polar coordinates and parametric equations, infinite sequences and series.

**MATH123F: Mathematical Deduction with Calculus**

This course is a first-year seminar. Topics covered include techniques and applications of integration and an introduction to sequences and series, with an emphasis on mathematical writing. Weekly papers will be required. It is suitable for students who have already taken calculus and are interested in pursuing the mathematics major. Students may not receive credit for both MATH 122 and 123.

**MATH 132: Elementary Statistics **

Statistics without calculus. Means, variance, and standard deviation. Distributions. Regression and correlation. Conditional probability.

**MATH 133:** **Intermediate Statistics**

This class continues the study of statistics begun in MATH 132. Topics will include experimental design, ANOVA, multiple regression, non-parametric tests, and further topics as time permits. This course is an ideal continuation for students who have taken MATH 132 or who got a 4 or 5 on the AP Statistics exam and who wish to deepen their statistics knowledge.

**MATH 211: Problem Solving for the Putnam **

This course will explore the problems and problem solving techniques of the annual William Lowell Putnam mathematical competition. Particular emphasis will be placed on learning to write clear and complete solutions to problems. The competition is open to all undergraduate students. The course is recommended for any student interested in taking the Putnam exam, held on the first Saturday in December.

**MATH 221: Vectors and Matrices **

Linear algebra from a geometric viewpoint. Vectors, matrices, linear equations, eigenvalues and eigenvectors. The possible math major is encouraged to take Math 223 instead of Math 221. The prerequisite is Math 122, or an advanced placement score of 4 or 5 on either AP calculus exam.

**MATH 222: Multivariable Calculus **

Calculus of functions of more than one variable, including vectors, lines, and planes; curves and surfaces in 2 and 3 dimensions; gradients, tangent planes, Lagrange multipliers; double and triple integrals; polar, cylindrical, and spherical coordinates; the theorems of Green, Stokes, and Gauss. The prerequisite is Math 122, or an advanced placement score of 4 or 5 on either AP calculus exam.

**MATH 223: Linear Algebra **

Linear algebra from an abstract viewpoint. Recommended for math majors instead of Math 221. Topics are similar, but proofs and conceptual understanding are stressed over geometric applications. The prerequisite is Math 122, or an advanced placement scores of 4 or 5 on either AP calculus exam.

**MATH 225: Fundamentals of Analysis **

Calculus from a rigorous, theoretical viewpoint, this course is one of the centerpieces of the math major. Proofs of all those theorems you take for granted in calculus, like the Intermediate and Extreme Value theorems. Real numbers, limits, comtinuity, sequences and series, differentiation, integration. Math 221 and Math 222, or Math 223 and Math 222 are the prerequisites.

**MATH 226: Complex Analysis **

Functions of a complex variable. The Cauchy integral theorem, residues, power series, Liouville's theorem, the fundamental theorem of algebra, contour integration. The prerequisite is Math 222 or Math 225.

**MATH 228: Discrete Mathematics**

A first course in discrete and combinatorial mathematics, this course is also an introduction to abstraction and proofs. The topics are variable, but may include induction, counting, set theory, number theory, complexity theory and graphs. The prerequisite is Math 221 or Math 223.

**MATH 229: Differential Equations **

Differential equations are of crucial importance in all applications of calculus. This course considers only ordinary differential equations. Constant coefficients, the Laplace transform, systems of equations, and series solutions. The prerequisite is Math 221 or Math 223.

**MATH 231: Probability **

This is a course in probability theory at an intermediate level. The subjects covered will include probability spaces, stochastic variables, mathematical expectation and variance, the law of large numbers, and the central limit theorem. The prerequisite is Math 222.

**MATH 232: An Introduction to Mathematical Statistics **

This course is at an intermediate level. The subjects covered will include statistical models, exponential families, sufficient statistics, estimators, regression, and testing statistical hypotheses. Some attention will be paid to robustness. The prerequisite is Math 231 and Math 221 or 223.

**MATH 241: Set Theory**

Posets, losets and wosets; ordinal and cardinal numbers; cardinal arithmetic; theorems of Cantor and Schroeder-Bernstein; cofinality; the Axiom of Choice and (some) other axioms of ZFC; applications to N, R, and their subsets. Some infinitary combinatorics. The prerequisite is Math 121 and 122.

**MATH 242: Topology **

Topology is the study of surfaces, in a very general sense. This class focuses on knots, which are embeddings of the circle into 3-dimensional space. We discuss common knots, such as the trefoil and the figure 8, and some common invariants of knots, such as the Jones polynomial and the genus.

**MATH 243: Mathematical Logic **

An introduction to mathematical logic, including first-order logic and model theory, axiomatic set theory, and Godel's incompleteness theorem. The prerequisite is Math 241 or Math 261 or Math 228.

**MATH 244: Topology: Point Set **

This is an introduction to general topology, the study of topological spaces. We will begin with the most natural examples, metric spaces, and then move on to more general spaces. This subject, fundamental to mathematics, enables us to discuss notions of continuity and approximation in their broadest sense. We will illustrate its power by seeing important applications to other areas of mathematics.

**MATH 251: Topics in Geometry: Geometric Analysis and Discrete Groups **

This will be an introduction to the theory of discrete groups, including hyperbolic geometry and the theory of Kleinian groups. Kleinian groups are easy to define, but their behavior can be quite complicated and beautiful. It is recommended that students take one of Math 225, Math 228, or Math 261 before taking Math 251.

**MATH 261: Abstract Algebra **

Along with Math 225, this is the centerpiece of the mathematics major. An introduction to groups, rings and fields. The prequisite is Math 221 or Math 223. It is recommended that students take Math 223 or Math 228 before taking Math 261.

**MATH 262: Abstract Algebra, Part II **

Continuation of Math 261. Modules, linear transformations, Galois theory. Students planning to go to graduate school in mathematics should take this course.

**MATH 271: Error Correcting Codes **

Nowadays messages are sent electronically through different kinds of communication channels. Most of these channels are not perfect and errors are created during the transmission. The goal of this course is to introduce the basic mathematical ideas lying behind the design of error correcting codes. The prerequisite is Math 221 or Math 223.

**MATH 272: Number Theory **

Fun with integers. Divisibility, congruences, quadratic residues, and Diophantine equations, following the immortal Gauss. The prerequisite is Math 221 or Math 223

**MATH 273: Combinatorics **

Generating functions, recurrence relations, inclusion-exclusion, and counting techniques. Basic graph theory, binomial coefficients, and platonic solids. The prerequisite is Math 223 or Math 228.

**MATH 274: Graph Theory **

A first course in graph theory with an emphasis on proofs and proof writing. The topics are variable, but usually include a discussion of trees, planar graphs, the Four Color Theorem, chromatic number, the n-dimensional hypercube, bipartite graphs and matching.

**MATH 283: Differential Geometry**

This course is an introduction to the classical differential geometry of curves and surfaces in Euclidean 3-space. Topics from global differential geometry and extensions to higher dimensions will be considered as time and the background of the students permit.