Course Catalog for MATHEMATICS
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 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. At the discretion of the Mathematics Department, section enrollments may be balanced. (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.
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 may include weighted and unweighted voting, fair division of resources, apportionment of goods and representatives, and personal decision-making algorithms based upon utility, risk, probability, expectation, and various game-theoretic strategies in general. Examples may be drawn from medicine, law, foreign policy, public policy, economics, psychology, sports, and gambling. At the discretion of the Mathematics Department, section enrollments may be balanced. (NUM)
Prerequisite: A satisfactory score on the Mathematics Placement Examination or a C- or better in Quantitative Literacy 101.
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 Pearls
An introduction to mathematical topics from logical thinking, sets, probability, geometry and art, and more. This course is not open to students with credit for Math 131, 142 or any Math course at the 200-level or above. (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 first-hand understanding of the political structures and processes behind the maps and shapes of Connecticut's Congressional and Assembly districts. (NUM)
C+ or better in QLIT-101 or a math placement score that has exempted the student from QLIT-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.
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 First-Year 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, 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.
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.
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, e-commerce, 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.
Prerequisite: A satisfactory score on the Mathematics Placement Examination, or C- or better in Mathematics 127.
0.50 units, Seminar
MATH 202
Introduction to Difference Equations and Discrete Models
This course is an introduction to basic concepts and techniques of difference equations for undergraduate students. Difference equations are generally used as models that describe the evolution of some system over time. They naturally appear as Discrete Analogues and numerical solutions of differential equations that model various phenomena in biology, ecology, physics, economics and other areas. For instance, difference equations frequently arise in computer science when determining the cost of an algorithm in big-O notation. In addition to performing mathematical analysis, the student will learn how to use technology (Matlab, Mathematics) to experiment simulations and discover equations and models that possess fascinating properties. (NUM)
Prerequisite: C- or better in Mathematics 132.
1.00 units, Lecture
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)
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 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.
Prerequisite: C- or better in Math 132 or equivalent and C- or better or concurrent registration in a 200-level math course.
0.50 units, Seminar
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.
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 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.
1.00 units, Lecture
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.
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.
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 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 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 in-depth 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 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.
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 254
Introduction to Mathematical Modeling, II
A companion to Mathematics 252, with an alternate set of topics and an emphasis on applications selected from the social sciences, especially economics. See description of Mathematics 252. Both Mathematics 252 and 254 may be taken for credit. (NUM)
Prerequisite: C- or better in Computer Science 115 and one year of calculus, or permission of instructor.
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.
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 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
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. (WEB)
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 308
Abstract Algebra II
A continuation of Mathematics 307. Further topics from group, ring, and field 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.
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 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 real-world 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 200-level math course, and permission of instructor.
1.00 units, Lecture
MATH 325
Special Topics in Algebra
Assuming no prior exposure to abstract algebra, this course provides a non-traditional introduction to general algebra. We cover such topics as monoids, semigroups, quasigroups, introductory universal algebra, and introductory category theory. Students who have already taken an abstract algebra course are welcome as well.
Prerequisite: C- or better in Mathematics 205, 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
Properties of the real number system, elementary topology, limits, continuity, uniform convergence, differentiation and integration of real-valued functions, sequences, and series of functions. At the discretion of the Mathematics Department, section enrollments may be balanced. (WEB)
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 332
Analysis II
Further topics which may include Fourier analysis, general integration theory, and complex analysis. (NUM)
Prerequisite: C- or better in Mathematics 331.
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.
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 466
Teaching Assistant
Submission of the special registration form, available in the Registrar’s Office, and the approval of the instructor and chairperson are required for enrollment.
0.50 units, Independent Study
MATH 497
Senior Thesis
Required of, but not limited to, honors candidates.
1.00 units, Independent Study
MATH 498
Senior Thesis Part I
No Course Description Available.
2.00 units, Independent Study
MATH 499
Thesis
No Course Description Available.
2.00 units, Independent Study