QLIT 101 
Foundational Techniques for Quantitative Reasoning 
This course offers students new insights into important and widely used mathematical concepts, with a strong focus on numerical and algebraic relationships. 
1.00 units, Lecture

MATH 103 
Introduction to Sports Analytics 
With the rise in the number of professional sports teams now hiring data scientists, sports and data have become inseparable. From player evaluation to ingame strategy, data analysis guides decision making in many different sports. Students in this course will develop strong computational skills while investigating the varied statistical techniques used in sports such as baseball, basketball, and football, including applications to college sports and gambling. In this handson course, students will complete projects using authentic data to gain a deeper understanding of the ways in which data informs decisions in sports. (NUM) Prerequisite: A satisfactory score on the Mathematics Placement Examination or a C or better in Quantitative Literacy 101. 
1.00 units, Lecture

MATH 105 
Graph Theory and Networks: Connections, Coverings, and Colorings 
Graph theory, which can be considered the study of connectedness within discrete structures, has numerous applications ranging from the sciences to the humanities, from monitoring electrical grids to understanding social networks. This course will focus on graphs and their substructures, and student learning will be handson and example driven. Topics will include spanning trees, coverings, coloring games, and their applications. (NUM) Prerequisite: A satisfactory score on the Mathematics Placement Examination or a C or better in Quantitative Literacy 101. Students who qualify or have credit for Mathematics 131 or 207 are not eligible to enroll in this course. 
1.00 units, Lecture

MATH 107 
Elements of Statistics 
A course designed primarily for students in the social and natural sciences. Topics include graphical methods, measures of central tendency and dispersion, basic probability, random variables, sampling, confidence intervals, and hypothesis testing. This course is not open to students with credit for Mathematics 131 or above, or who have placed into Mathematics 207 on the Mathematic Placement Examination (NUM) Prerequisite: A satisfactory score on the Mathematics Placement Examination or a C or better in Quantitative Literacy 101. Students who qualify or have credit for Mathematics 131 or 207 are not eligible to enroll in this course. 
1.00 units, Lecture

MATH 112 
An Introduction to Prison Gerrymandering in Connecticut and The Mathematics of
Redistricting 
This course will provide an introduction to the drawing electoral district lines and the mathematics behind gerrymandering. We will focus in particular on the notions of compactness and contiguity in relation to prison gerrymandering in Connecticut. Students will learn about the geometry of redistricting and voting theory to better understand the impact of prison gerrymandering. (NUM) 
0.50 units, Lecture

MATH 114 
Judgment and Decision Making 
In this course, we consider the application of elementary mathematical analysis to various procedures by which societies and individuals make decisions. Topics will include weighted and unweighted voting, apportionment of representatives, redistricting / gerrymandering, and game theory with a theme of understanding decisionmaking algorithms in the context of historic and modern politics in the United States and around the world. (NUM) Prerequisite: satisfactory score Mathematics Placement Examination or C+QLIT 101 
1.00 units, Lecture

MATH 117 
Introduction to Statistics 
This course will provide a basic foundation in descriptive and inferential statistics, including constructing models from data. Students will learn to think critically about data, apply discrete and continuous probability models, and utilize statistical inference procedures using computational tools. Topics include descriptive and inferential statistics, including one and twosample hypothesis testing, and single and multiple regression. The course is open to any student who has already satisfied the College's Quantitative Literacy requirement. (NUM) Prerequisite: A satisfactory score on the Mathematics Placement Examination or a C or better in Quantitative Literacy 101. Students who have credit for Mathematics 207 are not eligible to enroll in this course. 
1.00 units, Lecture

MATH 121 
Mathematics of Money 
An introduction to concepts related to financial mathematics. Topics will include simple interest, compound interest, annuities, investments, retirement plans, credit cards, and mortgages. A strong background in algebra is required. Not open to students who have received credit for Math 131 or higher. (NUM) Prerequisite: A suitable score on the Mathematics Placement Exam and completion of QLIT101 with a grade of C or better. 
1.00 units, Lecture

MATH 123 
Mathematical Gems 
An introduction to mathematical topics from number theory, geometry, game theory, infinity, chaos, and more. Not open to students who have received credit for Mathematics 131. (NUM) Prerequisite: A suitable score on the Mathematics Placement Exam and completion of QLIT101 with a grade of C or better. 
1.00 units, Lecture

MATH 127 
Functions, Graphs and Modeling 
This course will focus on the study of functions and graphs and their uses in modeling and applications. Emphasis will be placed on understanding the properties of linear, polynomial, rational piecewise, exponential, logarithmic and trigonometric functions. Students will learn to work with these functions in symbolic, graphical, numerical and verbal form. (NUM) Prerequisite: A satisfactory score on the Mathematics Placement Examination or a C or better in Quantitative Literacy 101. Students who qualify or have credit for Mathematics 131 or 207 are not eligible to enroll in this course. 
1.00 units, Lecture

MATH 128 
The Mathematics of Redistricting/Gerrymandering, Elections, and the U.S. Census 
This course will use mathematical tools to analyze redistricting and elections in Connecticut and in the United States. Students will learn about the mathematics and laws of redistricting/gerrymandering and their impact on the shapes of maps and elected candidates in national and state elections. To support these goals, students will learn about the mathematics of election forecasting, the U.S. Census, data analysis, and the geometric analysis of maps to understand the variety of components associated with the decennial redrawing of political districts. For the Community Learning component, students will interact with Connecticut legislators in Hartford to gain a firsthand understanding of the political structures and processes behind the maps and shapes of Connecticut's Congressional and Assembly districts. (NUM) Prerequisite: A satisfactory score on the Mathematics Placement Examination or a C or better in Quantitative Literacy 101. 
1.00 units, Seminar

MATH 131 
Calculus I Workshop 
The Calculus I Workshop is a challenging, interactive group learning environment for interested students. Each workshop is typically based on a detailed set of worksheets which students work through in an interactive setting. Students are encouraged to “talk mathematics”, thinking aloud and working with other students. Workshop problems are based on the material covered in lecture, but they are designed to stretch each student’s abilities to the fullest extent. The students spend most of the workshop time collaborating in groups, grappling with difficult ideas and problems. (NUM) Corequisite: Must be enrolled in Mathematics 131 concurrently. 
0.25 units, Laboratory

MATH 131 
Calculus I 
The real number system, functions and graphs, continuity, derivatives and their applications, antiderivatives, definite integrals, and the fundamental theorem of calculus. Mathematics, natural science, and computer science majors should begin the Mathematics 131, 132 sequence as soon as possible. Not open to students who have received credit by successful performance on the Advanced Placement Examination of the CEEB (see Catalogue section “Advanced Placement for FirstYear Students”). At the discretion of the Mathematics Department, section enrollments may be balanced. (NUM) Prerequisite: A satisfactory score on the Mathematics Placement Examination, or C or better in Mathematics 127. 
1.25 units, Lecture

MATH 132 
Calculus II 
Topics concerning the Riemann integral and its applications, techniques of integration, firstorder ordinary differential equations, and sequences and series. At the discretion of the Mathematics Department, section enrollments may be balanced. (NUM) Prerequisite: C or better in Mathematics 131, or an appropriate score on the AP Examination or Trinity's Mathematics Qualifying Examination. 
1.25 units, Lecture

MATH 132 
Calculus II Workshop 
The Calculus II Workshop is a challenging, interactive group learning environment for interested students. Each workshop is typically based on a detailed set of worksheets which students work through in an interactive setting. Students are encouraged to “talk mathematics”, thinking aloud and working with other students. Workshop problems are based on the material covered in lecture, but they are designed to stretch each student’s abilities to the fullest extent. The students spend most of the workshop time collaborating in groups, grappling with difficult ideas and problems. (NUM) 
0.25 units, Laboratory

MATH 160 
Using R for Data Visualization 
This course will provide an introduction to some of the visual methods used to handle and interpret big datasets such as those frequently collected in science, ecommerce, and government. Students will learn to use R Studio, a statistical programming environment, to explore large datasets and to communicate their results. Though the course does not assume any prior statistical or programming background, students should be comfortable with mathematical reasoning and logic. (NUM) Prerequisite: A satisfactory score on the Mathematics Placement Examination, or C or better in Mathematics 127. 
0.50 units, Seminar

MATH 205 
Abstraction and Argument 
This course deals with methods of proof and the nature of mathematical argument and abstraction. With a variety of results from modern and classical mathematics as a backdrop, we will study the roles of definition, example, and counterexample, as well as mathematical argument by induction, deduction, construction, and contradiction. This course is recommended for distribution credit only for nonmajors with a strong mathematical background. (NUM) 
1.00 units, Lecture

MATH 207 
Statistical Data Analysis 
An introductory course in statistics emphasizing modern techniques of data analysis: exploratory data analysis and graphical methods; random variables, statistical distributions, and linear models; classical, robust, and nonparametric methods for estimation and hypothesis testing; analysis of variance and introduction to modern multivariate methods. Those who successfully complete Math 107 may take Math 207 for credit due to its increased depth of coverage and breadth of topics. At the discretion of the Mathematics Department, section enrollments may be balanced. (NUM) Prerequisite: A suitable score on the Mathematics Placement Examination or a grade of C or better in Mathematics 107 or 127. 
1.00 units, Lecture

MATH 209 
Stochastic Processes 
An introduction to stochastic processes, including Markov chains, queueing
theory, and Monte Carlo simulations. Following the introduction of
conditional probability and expectation topics will include discrete Markov
chains, Poisson Processes, and continuous Markov chains. Limiting
behavior, stationary distributions, hitting times, and exit distributions will
emphasized throughout, along with applications and practical considerations
for Monte Carlo simulations. (NUM) Prerequisite: C or better in Mathematics 132. 
1.00 units, Lecture

MATH 210 
Scientific Computing in Matlab 
This course is a computational workshop designed to introduce the student to Matlab, a powerful scientific computing software package. The workshop will focus on visual learning based on graphical displays of scientific data and simulation results from a variety of mathematical subject areas, such as calculus, differential equations, statistics, linear algebra, and numerical analysis. No prior computer language skills are required as basic programming tools such as loops, conditional operators, and debugging techniques will be developed as needed. The workshop will prepare the student for future courses in applied mathematics as well as courses in other disciplines where scientific computing is essential. (NUM) Prerequisite: C or better in Math 132 or equivalent and C or better or concurrent registration in a 200level math course. 
0.50 units, Seminar

MATH 214 
Introduction to Combinatorics 
Topics may include, but are not limited to, basic counting methods including generating functions, recurrence relations and the principle of inclusion/exclusion, as well as an introduction to coding theory, graph theory and network optimization. (NUM) Prerequisite: C or better in Mathematics 132. 
1.00 units, Lecture

MATH 228 
Linear Algebra 
A proofbased course in linear algebra, covering systems of linear equations, matrices, determinants, finite dimensional vector spaces, linear transformations, eigenvalues, and eigenvectors. Students may not count both Mathematics 228 and Mathematics 229 for credit towards the Math major. (NUM) Prerequisite: C or better in Mathematics 132, 205, 231 or 253, or consent of instructor. 
1.00 units, Lecture

MATH 229 
Applied Linear Algebra 
An introduction to linear algebra with an emphasis on practical applications and computation. Topics will be motivated by realworld examples from a variety of disciplines, for instance medical imaging, quantum states, Google’s PageRank, Markov chains, graphs and networks,difference equations, and ordinary and partial differential equations. Topics will include solvability and sensitivity of large systems, iterative methods, matrix norms and condition numbers, orthonormal bases and the GramSchmidt process, and spectral properties of linear operators. MATLAB will be used for coding throughout the course, although no previous experience is required. Students may not count both Mathematics 228 and Mathematics 229 for credit towards the Math major. (NUM) Prerequisite: C or better in Mathematics 132, 205, 231 or 253, or consent of instructor. 
1.00 units, Lecture

MATH 231 
Calculus III: Multivariable Calculus 
Vectorvalued functions, partial derivatives, multiple integrals, conic sections, polar coordinates, Green's Theorem, Stokes' Theorem, and Divergence Theorem. At the discretion of the Mathematics Department, section enrollments may be balanced. (NUM) Prerequisite: C or better in Mathematics 132. 
1.25 units, Lecture

MATH 234 
Differential Equations 
An introduction to the theory of ordinary differential equation and their applications. Topics will include analytical and qualitative methods for analyzing firstorder differential equations, secondorder differential equations, and systems of differential equations. Examples of analytical methods for finding solutions to differential equations include separation of variables, variation of parameters, and Laplace transforms. Examples of qualitative methods include equilibria, stability analysis, and bifurcation analysis, as well as phase portraits of both linear and nonlinear equations and systems. At the discretion of the Mathematics Department, section enrollments may be balanced. (NUM) Prerequisite: C or better in Mathematics 132. 
1.00 units, Lecture

MATH 237 
Mathematics of Finance 
This is an introductory course on the mathematics of financial products, with a focus on options. The main topics include: mechanics and properties of options, option pricing in binomial models, the BlackScholes model, stochastic process, and the "Greeks". Equal emphasis is placed on proofs of formulas and the application of those formulas to pricing financial derivatives. Prerequisite: C or better in Mathematics 132 and 207, or permission of instructor (NUM) Prerequisite: C or better in Mathematics 132 and Mathematics 107 or permission of instructor. 
1.00 units, Lecture

MATH 241 
Number Systems, Sequences and Series 
This course covers the structure of the real line, sequences and limits, infinite series, including numerical and power series and special functions. Note that the treatment of sequences is designed with an eye towards having the necessary tools to study series in an indepth manner. Students who have earned credit for Mathematics 331 may not enroll in Mathematics 241. (NUM) Prerequisite: C or better in Mathematics 132. 
1.00 units, Lecture

MATH 252 
Introduction to Mathematical Modeling, I 
Application of elementary mathematics through firstyear calculus to the construction and analysis of mathematical models. Applications will be selected from the natural sciences and social sciences, with an emphasis on the natural sciences. Several models will be analyzed in detail, and the computer will be used as necessary. The analysis will consider the basic steps in mathematical modeling: recognition of the nonmathematical problem, construction of the mathematical model, solution of the resulting mathematical problems, and analysis and application of the results. Both Mathematics 252 and 254 may be taken for credit. (NUM) Prerequisite: C or better in Computer Science 115L and Mathematics 132. 
1.00 units, Lecture

MATH 253 
Number Theory and Its Application 
An introduction to the standard topics in number theory. Topics will include congruences, representation of integers, number theoretic functions, primitive roots, continued fractions and Pythagorean triples. Applications may include cryptology, primality testing, and pseudorandom numbers. (NUM) Prerequisite: C or better in Mathematics 132. 
1.00 units, Lecture

MATH 299 
Independent Study 
Submission of the special registration form, available in the Registrar’s Office, and the approval of the instructor and chairperson are required for enrollment. (NUM) 
0.50 units min / 2.00 units max, Independent Study

MATH 305 
Probability 
Discrete and continuous probability, combinatorial analysis, random variables, random vectors, density and distribution functions, moment generating functions, and particular probability distributions including the binomial, hypergeometric, and normal. At the discretion of the Mathematics Department, section enrollments may be balanced. (NUM) Prerequisite: C or better in Mathematics 231. 
1.00 units, Lecture

MATH 306 
Mathematical Statistics 
We consider confidence intervals and hypothesis testing from a theoretical viewpoint, with emphasis on sufficiency, completeness, minimum variance, the CramerRao lower bound, the RaoBlackwell theorem, and the NeymanPearson theorem. Other topics as time permits. (NUM) Prerequisite: C or better in Mathematics 305. 
1.00 units, Lecture

MATH 307 
Abstract Algebra I – Theory of Groups 
An introduction to group theory, including symmetric groups, homomorphism and isomorphisms, normal subgroups, quotient groups, the classification of finite abelian groups, the Sylow theorems. At the discretion of the Mathematics Department, section enrollments may be balanced.
**C or better in Mathematics 228 or Mathematics 229 and either Math 205/241 or permission of instructor.
**In addition, students must have earned a C+ or better in either Mathematics 228, 205 or 241. (WEB) Prerequisite: C or better in Mathematics 228 or 229 
1.00 units, Lecture

MATH 308 
Abstract Algebra II – Rings and Fields 
An introduction to rings and fields. Topics may include Groebner bases, field extensions, and Galois theory. (NUM) Prerequisite: C or better in Mathematics 307. 
1.00 units, Lecture

MATH 309 
Numerical Analysis 
Theory, development, and evaluation of algorithms for mathematical problem solving by computation. Topics will be chosen from the following: interpolation, function approximation, numerical integration and differentiation, numerical solution of nonlinear equations, systems of linear equations, and differential equations. Treatment of each topic will involve error analysis. (NUM) Prerequisite: C or better in Computer Science 115, MATH 132, and any mathematics course numbered 200 or higher. 
1.00 units, Lecture

MATH 314 
Combinatorics and Computing 
Introduction to combinatorics. Topics may include, but will not necessarily be limited to, computer representation of mathematical objects, enumeration techniques, sorting and searching methods, generation of elementary configurations such as sets, permutations and graphs, and matrix methods. (NUM) Prerequisite: C or better in Mathematics 228 or C or better in each of Mathematics 229 and either Math 205/241 or permission of instructor. 
1.00 units, Lecture

MATH 316 
Dynamical Systems 
An introduction to nonlinear dynamics and chaos theory, emphasizing qualitative methods for
both continuous and discrete dynamical systems. Topics will include fixed points and periodic
solutions, linearization and asymptotic behavior, existence and nonexistence theorems for
periodic orbits, and Floquet theory. Special emphasis will be placed on stability and bifurcation
analysis for parameterized families. The final part of the course will serve as an introduction to
chaos theory. Topics will include routes to chaos, strange attractors, selfsimilarity and fractal
dimensions, Lyapunov exponents, and renormalization. Modeling of realworld systems and
their applications will we stressed throughout the course. (NUM) Prerequisite: A grade of C or better in MATH 234; or Permission of the Instructor 
1.00 units, Lecture

MATH 318 
Topics in Geometry 
Differential geometry, projective geometry, nonEuclidean geometry, combinatorial topology, or such topics as the department may specify. May be repeated for credit with different topics. (NUM) Prerequisite: C or better in Mathematics 228 or C or better in each of Mathematics 229 and either Math 205/241 or permission of instructor. 
1.00 units, Lecture

MATH 325 
Special Topics in Applied Math 
An introduction to asymptotic analysis, which governs dominant behaviors of systems, and perturbation methods, which allow the analysis of effects of small changes. We explore how the relative size of contributing terms in a system can play a role in behaviors and solutions. This allows us to make simplifying assumptions and find approximate solutions in realworld scenarios, including vibrations of a mechanical rotor, pulsations of cardiac muscle tissue, and the nonlinear air drag on a projectile. Basic differential equations, numerical analysis, and possibly other course material will be included as necessary. Mathematical software may be introduced. This course is particularly relevant to aspiring applied mathematicians, engineers, and students in the Models and Data minor. Please see the professor for additional details. (NUM) Prerequisite: C or better in Math 132 or equivalent and C or better in a 200level math course, and permission of instructor. 
1.00 units, Lecture

MATH 326 
Graph Theory with Applications 
Introduction to the theory of graphs, with applications to real world problems. Topics may include, but are not necessarily restricted to: connectivity, paths and cycles, trees as information structures, digraphs and depthfirst search, stability and packing problems, matching theory and schedules, transportation networks, MaxFlowMinCut Theorem, planar graphs, color ability, and the four color problem. Admission to this course is usually contingent upon a student’s having credit for Mathematics 228. Offered in alternate years. (NUM) Prerequisite: C or better in Mathematics 228 or C or better in each of Mathematics 229 and either Math 205/241 or permission of instructor. 
1.00 units, Lecture

MATH 331 
Analysis I – Introduction to Real Analysis 
Properties of the real number system, elementary topology, limits, continuity, uniform convergence and differentiation of realvalued functions. (WEB) 
1.00 units, Lecture

MATH 332 
Analysis II – Measure and Integration 
This course further develops and explores topics and concepts from real analysis, with special emphasis on introducing students to subject matter and techniques that are useful for graduate study in mathematics. Topics may include the RiemannStieljes and Lebesgue integral, Lebesgue measure and spaces of continuous functions. (NUM) Prerequisite: C or better in Mathematics 331. 
1.00 units, Lecture

MATH 334 
Partial Differential Equations 
An introduction to partial differential equations and their applications. Topics will include physical laws, Fourier series, heat equations, wave equations, and other classical models. Students will learn to approach problems using both analytical and qualitative methods. The purpose of the course is to gain an understanding of how to construct mathematical models using reallife applications and to acquire the skills necessary to solve these problems appropriately. (NUM) Prerequisite: C or better in Mathematics 231 and 234, or permission of instructor. 
1.00 units, Lecture

MATH 341 
Complex Analysis 
Algebra of complex numbers, analytic functions and conformal mappings, integrals of analytic functions and Cauchy's theorem, expansion of analytic functions in series, calculus of residues. (NUM) Prerequisite: C or better in Mathematics 231. 
1.00 units, Lecture

MATH 399 
Independent Study 
Submission of the special registration form, available in the Registrar’s Office, and the approval of the instructor and chairperson are required for enrollment. (NUM) 
0.50 units min / 2.00 units max, Independent Study

MATH 400 
Senior Exercise 
A capstone course for senior math majors. Prerequisites: permission of instructor. (NUM) 
1.00 units, Lecture

MATH 401 
Lie Theory Through Matrix Groups 
This course will study the essential tools necessary for extending analysis to curved spaces via Lie Groups and Lie Algebras. The classical matrix groups and their associated algebras will be presented, introducing these in a concrete way as groups of rotations and then generalizing to more complex spaces Complex numbers and the quaternions will be also be introduced. (NUM) Prerequisite: C or better in Mathematics 331 or concurrent enrollment in Math 331, Senior status. 
1.00 units, Seminar

MATH 402 
Topology of Metric Spaces 
This course will introduce topology via metric spaces. Students will study many examples of metric spaces via sets in Euclidean space, and then generalize to sequence and function spaces. For each example, concepts such as connectedness, convergence, limit points, open and closed sets, and continuity of mappings will be studied. (NUM) Prerequisite: C or better in Mathematics 331 or concurrent enrollment in Math 331, Senior status. 
1.00 units, Seminar

MATH 403 
Fractal Geometry 
This course will study the emergence of fractal geometries in a variety of contexts. Fractals arising from iterated function systems, Julia and Mandelbrot sets, and strange attractors and bifurcation diagrams will be studied in detail Introductory topics from metric space analysis, complex analysis, and dynamical systems will be presented to allow for a rigorous treatment of each fractal type. (NUM) Prerequisite: C or better in Mathematics 228 or 229, at least one 300 level Mathematics course, Senior status. 
1.00 units, Seminar

MATH 404 
Discrete Nonlinear Dynamics 
This course will examine the nonlinear dynamics that emerge in discrete dynamical systems, i.e., iterative maps. Convergence will be rigorously treated in the context of fixed points, periodic orbits, quasiperiodic orbits, and chaotic attractors. Possible topics include the circle and standard maps, period doubling bifurcations and crises, chaotic dynamics and strange attractors, self similarity and fractals, and Hamiltonian chaos. (NUM) Prerequisite: C or better in Mathematics 228 or 229, at least one 300 level Mathematics course, Senior status. 
1.00 units, Seminar

MATH 405 
Continued Fractions 
This seminar will explore the number theoretic aspects of continued fractions as well as the analytic theory. Continued fractions in number theory will look at and help to explain naturally occurring phenomena such as eclipses, the lifecycle of cicadas as well as known rational approximations for pi and e. Techniques for approximating functions will be among those topics considered in the analytic theory of continued fractions. (NUM) Prerequisite: C or better in Mathematics 228 or 229, at least one 300 level Mathematics course, Senior status. 
1.00 units, Seminar

MATH 406 
Reading and Research 
This seminar is designed to be the apex of a student's (nonthesis) research endeavor and is available to students with a prior research experience (e.g., Summer Research Program or MATH 495). The seminar will consist of two main tasks. First, based on a prior research experience, students will prepare a rigorous mathematical writeup on their research in the format of a peerreviewed journal article. Second, students will choose a separate existing peerreviewed mathematical article to work through and replicate. This other article should be related to the student's own research and chosen in consultation with the faculty member who advised the student's research experience. (NUM) 
1.00 units, Seminar

MATH 409 
Mathematical Optimization 
This course will cover topics on optimization and study corresponding algorithms. Methods such as Newton's, conjugate gradient and quasiNewton will be included, and application to various optimization problems will be discussed. The course will extend to optimization for machine learning and carry out some simple exercises. Students are expected to understand the mathematical theorem for optimization and learn to apply the method using existing packages or creating their own codes. (NUM) Prerequisite: C or better in Mathematics 228 or 229, at least one 300 level Mathematics course, Senior status. 
1.00 units, Seminar

MATH 411 
Origins of Mathematics 
With attention to both rigorous proof and mathematical imagination, we
consider the development of modern mathematics, beginning with the clay
tablets of Mesopotamia that reveal hints of trigonometry and the Pythagorean
theorem. We then turn to the Greek invention of axiomatic mathematics as
presented in Euclid's Elements, with emphasis on the geometric proofs of
newlydiscovered incommensurability and the controversy of the 5th parallel
postulate. Finally, we trace the history and false proofs of Euclid's 5th
parallel postulate up through the late 1700s, concluding with the derivations
of properties of spherical and hyperbolic nonEuclidean geometries that were
independently discovered by Gauss, Bolyai, and Lobachevsky. (NUM) This course is open to seniors only. 
1.00 units, Seminar

MATH 426 
Spectral Graph Theory 
This course will focus on linear algebra and its applications to graph theory. We begin by studying classical results relating the eigenvalues and eigenvectors of the adjacency matrix and graph Laplacian matrix to properties of the underlying graph. We will also explore the connection between harmonic functions and applications to random walks on graphs, circuits, mechanical systems, and various special topics, time permitting. (NUM) This course is open to seniors only. 
1.00 units, Seminar

MATH 453 
Analytic Number Theory 
A study of topics from the classical analytic theory of numbers. Analytic tools will be used to study topics such as arithmetic functions, the distribution of primes, congruences, the Riemannzeta function, the prime number theorem, Eisenstein series, quadratic residues, Dirichlet series, Euler products, the Jacobi theta functions, integer partitions, and modular forms (NUM) Prerequisite: C or better in Mathematics 307, 331, or 341, senior status, or consent of instructor. 
1.00 units, Seminar

MATH 466 
Teaching Assistant 
Submission of the special registration form, available online, and the approval of the instructor are required for enrollment. Guidelines are available in the College Bulletin.
(0.5  1 course credit) 
0.50 units, Independent Study

MATH 490 
Research Assistant 
This course is designed to provide students with the opportunity to undertake substantial research work with a faculty member. Students need to complete a special registration form, available online, and have it signed by the supervising instructor. 
0.50 units min / 1.00 units max, Independent Study

MATH 497 
Senior Thesis 
Required of, but not limited to, honors candidates. Submission of the special registration form and the approval of the instructor and director are required for this course. (NUM) 
1.00 units, Independent Study

MATH 498 
Senior Thesis Part I 
This course is the first part of a two semester, two credit thesis. Submission of the special registration form and the approval of the thesis adviser and the director are required for enrollment. The registration form is required for each semester of this yearlong thesis. (NUM) 
1.00 units, Independent Study

MATH 499 
Thesis 
This course is the second part of a two semester, two credit thesis. Submission of the special registration form and the approval of the thesis adviser and the director are required for enrollment. The registration form is required for each semester of this yearlong thesis. (NUM) 
1.00 units, Independent Study
