MATH 1060a, The Shape of Space  Tim Ablondi

This course provides an introduction to mathematical thinking through ideas in geometry and graph theory. Traditional lecture, worksheets, discussion, group work, and classroom activities all contribute to a dynamic learning experience. The course follows a historical narrative, starting from antiquity, to understand the foundations of mathematical thought. An axiomatic approach to geometry affords students the opportunity to construct proofs of classical theorems. The basics of graph theory are introduced in order to explore real world problems such as map coloring and bridge crossing. The ancient Greek method of exhaustion previews a discussion of the integral, and from here we explore the beautiful relationship between the geometry and topology of graphs, polyhedra, and surfaces. Throughout the course students build their mathematical and geometric intuition through problem solving and exercises in geometric imagining. Permission of instructor required. Enrollment limited to 25 students who have not previously taken a high school or college calculus course.   QR
TTh 11:35am-12:50pm

* MATH 1100a, Introduction to Functions and Calculus I  Laura Seaberg

Comprehensive review of precalculus, limits, differentiation and the evaluation of definite integrals, with applications. Precalculus and calculus topics are integrated. Emphasis on conceptual understanding and problem solving. Successful completion of MATH 1100 and 1110 is equivalent to MATH 1120. No prior acquaintance with calculus is assumed; some knowledge of algebra and precalculus mathematics is helpful. The course includes mandatory weekly workshops, scheduled at the beginning of term. Placement into MATH 1100 on the Mathematics placement exam is required. May not be taken after MATH 1110-1210.   QR
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* MATH 1120a, Calculus of Functions of One Variable I  Meghan Anderson

This course introduces the notions of derivative and of definite integral for functions of one variable, with some of their physical and geometrical motivation and interpretations. Emphasis is placed on acquiring an understanding of the concepts that underlie the subject, and on the use of those concepts in problem solving. This course also focuses on strategies for problem solving, communication and logical reasoning. Placement into MATH 1120 on the Mathematics placement exam is required. No prior acquaintance with calculus or computing assumed. May not be taken after MATH 1110, or after MATH 1150-1210.   QR
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* MATH 1150a, Calculus of Functions of One Variable II  Sarah Days-Merrill

A continuation of MATH 1120, this course develops concepts and skills at the foundation of the STEM disciplines. In particular, we introduce Riemann sums, integration strategies, series convergence, and Taylor polynomial approximation. We use these tools to measure lengths of parametric curves, areas of polar regions and volumes of solids of revolution, and we explore applications of calculus to other disciplines including physics, economics, and statistics. MATH 1150 also focuses on strategies for problem solving, communication, and logical reasoning. Prerequisite: MATH 1110 or MATH 1120, or placement into MATH 1150 on the Mathematics placement exam. May not be taken after MATH 1160 - 1210.   QR
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MATH 2220a / AMTH 2220a, Linear Algebra with Applications  Staff

Matrix representation of linear equations. Gauss elimination. Vector spaces. Linear independence, basis, and dimension. Orthogonality, projection, least squares approximation; orthogonalization and orthogonal bases. Extension to function spaces. Determinants. Eigenvalues and eigenvectors. Diagonalization. Difference equations and matrix differential equations. Symmetric and Hermitian matrices. Orthogonal and unitary transformations; similarity transformations. Students who plan to continue with upper level math courses should instead consider MATH 2250 or 2260. After MATH 1150 or equivalent. May not be taken after MATH 2250 or 2260. May not be counted toward the Math, CPSC + Math, or Econ + Math major.   QR
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MATH 2410a / S&DS 2410a, Probability Theory  Sinho Chewi

Introduction to probability theory. Topics include probability spaces, random variables, expectations and probabilities, conditional probability, independence, discrete and continuous distributions, central limit theorem, Markov chains, and probabilistic modeling. After or concurrently with MATH 120 or equivalent.  QR
MW 9am-10:15am

MATH 2420b / S&DS 2420b, Theory of Statistics  Zhou Fan

Study of the principles of statistical analysis. Topics include maximum likelihood, sampling distributions, estimation, confidence intervals, tests of significance, regression, analysis of variance, and the method of least squares. Some statistical computing. After S&DS 241 and concurrently with or after MATH 222 or 225, or equivalents.  QR
MW 2:35pm-3:50pm

MATH 2440a / AMTH 2440a, Discrete Mathematics  Catherine Wolfram

Basic concepts and results in discrete mathematics: graphs, trees, connectivity, Ramsey theorem, enumeration, binomial coefficients, Stirling numbers. Properties of finite set systems. Prerequisite: MATH 1150 or equivalent. Some prior exposure to proofs is recommended (ex. MATH 2250).  QR
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MATH 2510b / EENG 434 / S&DS 3510b, Stochastic Processes  Shuangping Li

Introduction to the study of random processes including linear prediction and Kalman filtering, Poison counting process and renewal processes, Markov chains, branching processes, birth-death processes, Markov random fields, martingales, and random walks. Applications chosen from communications, networking, image reconstruction, Bayesian statistics, finance, probabilistic analysis of algorithms, and genetics and evolution. Prerequisite: S&DS 241 or equivalent.  QR
MW 1:05pm-2:20pm

* MATH 3200a, Measure Theory and Integration  Michail Louvaris

Construction and limit theorems for measures and integrals on general spaces; product measures; Lp spaces; integral representation of linear functionals. After MATH 3050 or equivalent.  QR
MW 1:05pm-2:20pm

MATH 3220a / AMTH 3220a / CPSC 4844a, Geometric and Topological Methods in Machine Learning  Smita Krishnaswamy

This course provides an introduction to geometric and topological methods in data science. Our starting point is the manifold hypothesis: that high dimensional data live on or near a much lower dimensional smooth manifold. We introduce tools to study the geometric and topological properties of this manifold in order to reveal relevant features and organization of the data. Topics include: metric space structures, curvature, geodesics, diffusion maps, eigenmaps, geometric model spaces, gradient descent, data embeddings and projections, and topological data analysis (TDA) in the form of persistence homology and their associated “barcodes.” We see applications of these methods in a variety of data types.  Prerequisites: MATH 2250 or 2260; MATH 2550 or 2560; MATH 3020; and CPSC 1001 or equivalent programming experience.   QR, SC
TTh 11:35am-12:50pm

MATH 3300a / S&DS 4000a, Advanced Probability  Shuangping Li

Measure theoretic probability, conditioning, laws of large numbers, convergence in distribution, characteristic functions, central limit theorems, martingales. Some knowledge of real analysis assumed.  QR
TTh 2:35pm-3:50pm

MATH 3800a, Algebra  Samuel DeHority

The course serves as an introduction to commutative algebra and category theory. Topics include commutative rings, their ideals and modules, Noetherian rings and modules, constructions with rings, such as localization and integral extension, connections to algebraic geometry, categories, functors and functor morphisms, tensor product and Hom functors, projective modules. Other topics may be discussed at instructor's discretion.  After MATH 3500 and 3700.  QR
MW 9am-10:15am

MATH 4210a / AMTH 4200a, The Mathematics of Data Science  Gilles Mordant

This course aims to be an introduction to the mathematical background that underlies modern data science. The emphasis is on the mathematics but occasional applications are discussed (in particular, no programming skills are required). Covered material may include (but is not limited to) a rigorous treatment of tail bounds in probability, concentration inequalities, the Johnson-Lindenstrauss Lemma as well as fundamentals of random matrices, and spectral graph theory.  Prerequisite: MATH 3050.   QR, SC
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