Math 411 : Commutative Algebra
An introduction to rings and modules.
Math 327T : Tiling Theory
An introduction to the mathematical theory of tiles, including two-dimensional and three-dimensional tiles and aperiodic tiles.
Math 313T : Explorations in Number Theory and Geometry
A tutorial that focuses on the beautiful and powerful interactions between number theory and geometry, including elliptic curves and the geometry of numbers.
Math 307 : Methods in Mathematical Modeling and Operations Research
This course focuses on optimization techniques, including linear programming and integer programming. Departing from the deterministic realm, we will discuss dynamic programming, statistical machine learning, and epidemiological modeling.
Stat 441 : Bayesian Statistics
Statistics which make use of subjective (as opposed to frequentist) probability.
Math 433 : Mathematical Modeling and Control Theory
Mathematical modeling is concerned with translating a natural phenomenon into a mathematical form. In this abstract form the underlying principles of the phenomenon can be carefully examined and real-world behavior can be interpreted in terms of mathematical shapes. The models we investigate include feedback phenomena, phase locked oscillators, multiple population dynamics, reaction-diffusion equations, shock waves, morphogenesis, and the spread of pollution, forest fires, and diseases. Many of these systems allow for some aspect of control, and we will investigate how to operate such controls in order to achieve a specific goal or optimize measures of performance.
Math 401 : Functional Analysis with Applications to Mathematical Physics
Functional analysis can be viewed as linear algebra on infinite dimensional spaces. This course will study linear operators on Hilbert spaces and their spectral properties. A special attention will be dedicated to various operators arising from mathematical physics-especially the Schrodinger operator.
Math 373 : Investment Mathematics
The 1997 Nobel Prize in Economics was awarded to Robert Merton and Myron Schloles for their Black-Scholes model of the value of financial instruments. This course will study deterministic and random models, futures, options, the Black-Scholes Equation, and additional topics.
Stat 358T : Introduction to Biostatistics
Statistical methods for the analysis of data from medical research, biology and clinical trials. Linear and Logistic Regression. ANOVA and contingency table analysis.
Math 317 : Applied Abstract Algebra
Groups, Rings and Fields with an emphasis on their applications.
Math 313 : Introduction to Number Theory
The study of numbers dates back thousands of years, and is fundamental in mathematics. In this course, we will explore the integers, and examine issues involving primes, divisibility, and congruences. We will also look at the ideas of number and prime in more general settings.
Math 306 : Chaos and Fractals
An introduction to the mathematics of chaos and fractals.
Math 251T : Introduction to Mathematical Proof and Argumentation
Acquiring the ability to create and clearly express mathematical arguments through an exploration of topics from discrete mathematics including logic, number theory, infinity, geometry, graph theory, and probability. Our goal is not only to gain an understanding and appreciation of interesting and important areas of mathematics but also to develop and critically analyze original mathematical ideas and argumentation.
Math 211T : Mathematical Reasoning and Linear Algebra
This tutorial introduces students to problem-solving and proof-writing techniques through the use of linear algebra.
Math 414 : Galois Theory
Galois theory is the intriguing story of the interplay between
polynomials, groups, and fields. The crowning jewel of Galois theory is the beautiful correspondence between subgroups of the Galois group and intermediate fields of the extension. The most famous application of the theory is the proof of the insolvability of the quintic (and, in fact, all polynomials of degree at least 5).
Math 404 : Ergodic Theory
An introduction to notions of randomness in dynamical systems using tools from measure theory.
Math 316 : Protecting Information: Applications of Abstract Algebra and Quantum Physics
Classical Cryptography and Error Correction, Quantum Cryptography and Computation.
Stat 421 : Introduction to Categorical Data Analysis
Analysis and models for binary and count response data through contingency tables and logistic and loglinear models.
Math 403 : Irrationality and Transcendence
We explore the classical theory of transcendental number theory and prove such important results as the Lindemann-Weierstrass Theorem, Siegel’s Lemma and the Gelford-Schneider Theorem. We also study the Weierstrass zeta-function and Mahler’s class. function.
Math 321 : Knot Theory
An introduction to the mathematical theory of knots, including various types of knots, methods of tabulating knots and invariants for distinguishing knots.
Math 426 : Hyperbolic 3-Manifold
An introduction to 3-manifolds with constant negative curvature, the surfaces within them and the invariants associated with them.
Stat 442 : Computational Statistics and Data Mining
In this course we will investigate new methodologies in Statistics that are capable of analyzing the large data sets that are common in science and industry today. Traditional techniques in statistics are often unable to cope with the size and complexity of these data bases and warehouses.The methods we will study are designed to address these inadequacies, emphasizing visualization, exploration and empirical model building. Real data sets will be analyzed from such areas as consumer web data, genomics, and finance.
Math 425 : Geometric Measure Theory
Geometric measure theory uses measure theory to generalize differential geometry to surfaces and spaces with unpredictable singularities, such as junctures in soap bubble clusters, defects in materials, and black holes in the universe.
Math 418 : Matrix Groups
Matrix groups, Lie algebras, matrix exponentiation, maximal tori, Weil groups.
Math 335T : Biological Modeling and Differential Equations
Differential equation models have been used to explain many biological phenomena including fluctuations in food webs, the spread of disease, consequences of fishing practices, immune system response to infection, spatial distribution of species, formation of zebra stripes, and flux across cell membranes. Through these models the students will be introduced to the field of mathematical biology in a small group tutorial format.
Math 314 : Polynomial Arithmetic
Polynomials behave like integers in many ways. Although
number theory is typically thought of as the study of the integers, most number-theoretic questions about the integers can be reformulated in terms of polynomials. In fact, sometimes the answers are much easier to discover for the polynomials. In this course, we’ll examine the arithmetic properties of polynomials over a finite field including the analogy with the integers.
Math 413 : An Introduction to p-Adic Analysis
We investigate the algebraical and analytical structure of the p-adic numbers and study applications to number theory.
Math 323 : Applied Topology
An introduction to topology with emphasis on recent applications, including economics, geographic information systems, cosmology, chaos and others.
Math 417 : Algebraic Error Correcting Codes
An introduction to linear codes including Generalized Reed-Solomon codes.
Math 415 : Geometric Group Theory
Associating geometric models to algebraic structures, polyhedral tilings, braids, Coxeter groups.
Math 327 : Computational Geometry
Polyhedral curvature, voronoi diagrams, robotics, origami, cartography, triangulations.