Course Descriptions

Course Catalog for MATHEMATICS
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.
Prerequisite: A satisfactory score on the Mathematics Placement Examination. Students who qualify for Mathematics 131 or 207 will not be eligible to enroll in this course.
1.00 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, economics, psychology, sports, and gambling.
Prerequisite: A satisfactory score on the Mathematics Placement Exam
1.00 units, Lecture
MATH 118
Mathematics of Games and Gambling
We introduce at an elementary level the mathematics necessary to analyze and understand games of strategy and chance, including: lotteries, poker, craps, tournaments, the prisoner’s dilemma, and the Monte Hall problem.
Prerequisite: A satisfactory score on the Mathematics Placement Exam
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.
Prerequisite: A satisfactory score on the Mathematics Placement Exam
1.00 units, Lecture
MATH 123
Mathematical Pearls
An introduction to mathematical topics from logical thinking, sets, probability, geometry and art, and more.
1.00 units, Lecture
MATH 125
Functions and Limits
The sequence Mathematics 125-126 provides an opportunity to study differential calculus while simultaneously covering the needed skills from precalculus. Students who finish both Mathematics 125 and 126 will be prepared to take Mathematics 132, Calculus II. Topics in Mathematics 125 will include: the real number system; linear, quadratic, polynomial, rational, exponential, and trigonometric functions; equations and inequalities; limits and continuity; applications. Not open to students who have received credit for Mathematics 131. Ordinarily, this course, to be followed by Mathematics 126, is elected by students who need to take a course in calculus, but whose backgrounds in algebra and trigonometry need strengthening.
Prerequisite: A satisfactory score on the Mathematics Placement Examination. Students who qualify for Mathematics 131 or 207 will not be eligible to enroll in this course.
1.00 units, Lecture
MATH 126
Calculus with Algebra and Trigonometry
A continuation of Mathematics 125. Topics will include: the analytic geometry of lines, circles, and parabolas; functions and graphs; continuity; derivatives; and applications. Not open to students who have received credit for Mathematics 131. This course completes the sequence started in Mathematics 125. Together, Mathematics 125 and 126 combine a study of the differential calculus of functions of one variable with the necessary algebraic and trigonometric background.
Prerequisite: C- or better in Mathematics 125.
1.00 units, Lecture
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 for Mathematics 126 or who have received credit by successful performance on the Advanced Placement Examination of the CEEB (see Catalogue section “Advanced Placement for First-Year Students”).
Prerequiste: A satisfactory score on the Mathematics Placement Examination.
1.25 units, Lecture
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 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 132
Calculus II
Topics concerning the Riemann integral and its applications, techniques of integration, first-order ordinary differential equations, and sequences and series.
Prerequisite: C- or better in Mathematics 126 or 131, or an appropriate score on the AP Examination or Trinity's Mathematics Qualifying Examination.
1.25 units, Lecture
MATH 142
Accelerated Calculus II
This course is an accelerated version of Mathematics 132, which will cover in greater depth topics from that course, along with selected other topics from single-variable calculus. It is intended for those with strong Calculus I backgrounds; in particular, first-year students who have received credit via the Calculus AB Advanced Placement Examination should register for this course. Open to other students with permission of the instructor. See the description of Mathematics 132.
Prerequisite: C- or better in Mathematics 126 or 131, or an appropriate score on the AP Examination or Trinity's Mathematics Qualifying Examination.
1.25 units, Lecture
MATH 201
Problem Solving in Mathematics
Problems appear in every part of mathematics and often have an intrinsic beauty and appeal. Mathematical problem solving is not a distinct branch of mathematics, but rather is a “mindset” which combines results from all branches of mathematics with a collection of useful techniques and strategies. Attempts have been made to develop “systems” for problem solving, but for the most part facility is gained through experience. The purpose of this course is to develop skills in and foster an appreciation of mathematical problem solving. It will not be a “cookbook” course which teaches students to match stereotypical problems with canned solutions. Rather, the course will be a hands-on experience, and students will be expected to explore and present solutions to a wide variety of non-routine and challenging problems, both individually and in groups. Since the range of problems which a student can solve expands as a student masters more branches of mathematics, students can profitably repeat this course. This course may only be taken Pass/Fail and may be retaken for credit with permission of the department.
Prerequisite: C- or better in Mathematics 126 or 131, or an appropriate score on the AP Examination or Trinity's Mathematics Qualifying Examination.
0.50 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.
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. Students with a strong mathematical background are advised to take Math 207 in place of Math 107. Those who successfully complete Math 107 may take Math 207 for credit due to its increased depth of coverage and breadth of topics.
Prerequisite: A suitable score on the Mathematics Placement Examination or a grade of C- or better in Mathematics 107..
1.00 units, Lecture
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.
Prerequisite: C- or better in Mathematics 142 or 132, or a 200-level mathematics course, or permission 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.
Prerequisite: C- or better in Mathematics 132 or 142.
1.25 units, Lecture
MATH 234
Differential Equations
An introduction to techniques for solving ordinary differential equations. Series solutions, initial value problems, and Laplace transforms.
Prerequisite: C- or better in Mathematics 132 or 142.
1.00 units, Lecture
MATH 241
Mathematics of Finance
An introduction to the basic mathematical tools used in the financial world. Topics may include simple and compound interest, periodic loans, present and future value, amortization, sinking funds, bonds and money market funds, tax-exempt, and tax-deferred investments. Life annuities, perpetual annuities, and the mechanics of life insurance. Students may also do calculations and modeling using spreadsheets; instructions on their use will be given as needed. Basic ideas from probability theory will also be introduced as needed. Additional topics may include linear programming, finite differences, and some actuarial mathematics. However, this course does not prepare students for the examinations of the Society of Actuaries.
Prerequisite: C- or better in Mathematics 132 or 142 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.
Prerequisite: C- or better in Computer Science 115L and Mathematics 132 or 142.
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.
Prerequisite: C- or better in Mathematics 132 or 142.
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.
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.
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.
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.
Prerequisite: C- or better in Mathematics 228 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.
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.
Prerequisite: C- or better in Computer Science 115, either MATH 132 or MATH 142, 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.
Prerequisite: C- or better in Mathematics 228 or permission of 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.
Prerequisite: C- or better in Mathematics 228 and 231.
1.00 units, Lecture
MATH 318
The Geometry of Spacetime: The Mathematics
This course is an introduction to the mathematics of special and general relativity. No previous knowledge of physics is required. This course will introduce the concept of spacetime and the state of Galilean relativity, and shall touch upon the mathematical contradictions presented by the results of the Michelson-Morley experiment and the classical Maxwell equations. Further topics include Einstein’s solution to special relativity, the development of Minkowski spacetime , the physical consequences of special relativity, relativistic kinetics, and the differential geometry required to describe this mathematically. The remainder of the course will cover the differential geometry necessary to understand De Sitter spacetime and the general relativistic equations of motion, including the differential geometry of curves and surfaces, curvature of surfaces, and geodesics.
Prerequisite: C- or better in Mathematics 228 or permission of instructor.
1.00 units, Lecture
MATH 325
Special Topics in Mathematical Biology
This course provides an introduction to the development, application, and evaluation of biological models. Both deterministic and stochastic models will be developed through a case-study based approach at the molecular, cellular, and population levels. Topics include current application areas such as neurophysiology, cardiology, cellular dynamics and gene expression, spread of infectious diseases, conservation of endangered species, and cancer growth. Theory from differential equations, statistics, scientific computing, and linear algebra will be introduced as needed with topics to include basic modeling principles, discrete-time models, matrix models, dynamical systems techniques, Markov chains, pattern formation, and agent-based models. When necessary, students will implement models using a high-level programming language as well as engage with current biology research literature.
Prerequisite: C- or better in a 200 level Mathematics course and permission of instructor.
1.00 units, Lecture
MATH 325
Special Topics in Analysis
A course which will be offered from time to time to meet the special needs and interests of mathematics students.
1.00 units, Lecture
MATH 325
Special Topics in Continued Fractions
No Course Description Available.
1.00 units, Lecture
MATH 325
Special Topics in Algebra
No Course Description Available.
1.00 units, Lecture
MATH 325
Special Topics in Graph Theory
No Course Description Available.
1.00 units, Lecture
MATH 325
Special Topics in Geometry
No Course Description Available.
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.
Prerequisite: C- or better in Mathematics 228 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.
Prerequisite: C- or better in Mathematics 228 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.
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.
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.
1.00 units, Lecture
MATH 419
Research Assistant
Submission of the special registration form, available in the Registrar's Office, and the approval of the instructor are required for enrollment.
1.00 units, Independent Study
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 490
Research Assistant
No Course Description Available.
0.50 units min / 1.00 units max, Independent Study
MATH 497
Senior Thesis
Required of, but not limited to, honors candidates.
1.00 units, Independent Study