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 or a C or better in Quantitative Literacy 101. 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 decisionmaking algorithms based upon utility, risk, probability, expectation, and various gametheoretic 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. This course is not open to students with credit for Math 131, 142 or any Math course at the 200level or above. 
1.00 units, Lecture 
MATH 125 
Functions and Limits 
The sequence Mathematics 125126 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 or a C or better in Quantitative Literacy 101. 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 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. Prerequisite: A satisfactory score on the Mathematics Placement Examination or a C or better in Quantitative Literacy 101. Students who qualify for Mathematics 131 or 207 will not be eligible to enroll in this course. 
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 FirstYear Students”). Prerequiste: A satisfactory score on the Mathematics Placement Examination, or Mathematics 127. 
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, firstorder 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 singlevariable calculus. It is intended for those with strong Calculus I backgrounds; in particular, firstyear 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 handson experience, and students will be expected to explore and present solutions to a wide variety of nonroutine 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 nonmajors 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, 127 or 131. 
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 200level math course. 
0.50 units, Seminar 
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. Prerequisite: C or better in Mathematics 132, 142, 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. Prerequisite: C or better in Mathematics 132 or 142. 
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. Prerequisite: C or better in Mathematics 132 or 142. 
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. Prerequisite: C or better in Mathematics 132 or 142, and a C or better, or concurrent enrollment in, Mathematics 205 or 228 
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. 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 CramerRao lower bound, the RaoBlackwell theorem, and the NeymanPearson 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 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. Prerequisite: A grade of C or better in MATH 234; or Permission of the Instructor 
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 MichelsonMorley 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 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. Prerequisite: C or better in Mathematics 228 and 231. 
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 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 casestudy 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, discretetime models, matrix models, dynamical systems techniques, Markov chains, pattern formation, and agentbased models. When necessary, students will implement models using a highlevel 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 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. 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 realvalued 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 

