| 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. |
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1.00 units, Lecture
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| 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 in-game 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 hands-on 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 or QLIT 103 |
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1.00 units, Lecture
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| 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 hands-on 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 or QLIT 103. Students who qualify or have credit for Mathematics 131 or 207 are not eligible to enroll in this course. |
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1.00 units, Lecture
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| 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 decision-making 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 or QLIT 103 |
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1.00 units, Lecture
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| 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 two-sample 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 suitable score on the Mathematics Placement Exam or completion of QLIT101 or QLIT 103 with a grade of C- or better. |
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1.00 units, Lecture
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| 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 or completion of QLIT101 or QLIT 103 with a grade of C- or better. |
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1.00 units, Lecture
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| 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 or completion of QLIT101 or QLIT 103 with a grade of C- or better. |
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1.00 units, Lecture
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| 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 or QLIT 103. Students who qualify or have credit for Mathematics 131 or 207 are not eligible to enroll in this course. |
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1.00 units, Lecture
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| 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 first-hand 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 or QLIT 103 |
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1.00 units, Seminar
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| 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. |
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0.25 units, Laboratory
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| 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 College Board AP exams (see Catalogue section “College Board AP Exams”). 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. |
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1.25 units, Lecture
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| MATH 132 |
| Calculus II |
Topics concerning the Riemann integral and its applications, techniques of integration, first-order 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. |
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1.25 units, Lecture
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| 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 non-majors with a strong mathematical background. (NUM) |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| 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 200-level math course. |
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0.50 units, Seminar
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| 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. |
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1.00 units, Lecture
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| MATH 228 |
| Linear Algebra |
A proof-based 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. |
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1.00 units, Lecture
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| MATH 229 |
| Applied Linear Algebra |
An introduction to linear algebra with an emphasis on practical applications and computation. Topics will be motivated by real-world 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 Gram-Schmidt 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. |
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1.00 units, Lecture
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| MATH 231 |
| Calculus III: Multivariable Calculus |
Vector-valued 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. |
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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 first-order differential equations, second-order 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. |
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1.00 units, Lecture
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| 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 Black-Scholes 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 252 |
| Introduction to Mathematical Modeling, I |
Application of elementary mathematics through first-year 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 non-mathematical 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. |
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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. |
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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 Cramer-Rao lower bound, the Rao-Blackwell theorem, and the Neyman-Pearson 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, self-similarity and fractal
dimensions, Lyapunov exponents, and renormalization. Modeling of real-world 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, non-Euclidean 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 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 depth-first search, stability and packing problems, matching theory and schedules, transportation networks, Max-Flow-Min-Cut 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 real-valued 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 Riemann-Stieljes 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 real-life 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 (non-thesis) 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 write-up on their research in the format of a peer-reviewed journal article. Second, students will choose a separate existing peer-reviewed 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 quasi-Newton 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
newly-discovered 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 non-Euclidean 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 Riemann-zeta 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 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 year-long 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 year-long thesis. (NUM) |
|
1.00 units, Independent Study
|