| MATH 101 |
| Contemporary Applications: Mathematics for the 21st Century |
| This course offers students new insights into fundamental mathematical concepts as they apply to a variety of current local and national issues. Areas of concentration are numerical, statistical, algebraic, and logical relationships. Three hours of lecture and one hour of laboratory per week. |
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1.00 units, Lecture
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| MATH 102 |
| Cityscape: Analyzing Urban Data |
| This course offers students an opportunity to strengthen their numerical and statistical reasoning abilities. The process of collecting, measuring, displaying, and interpreting data will be studied using data from current local and national sources. Three hours of lecture per week for one-half of the semester. |
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0.50 units, Lecture
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| MATH 102 |
| Newsmath: Logic and Statistics in the Media |
| Can you believe everything you read? This course will examine the basic principles of quantitative argument and reasoning, including statistics and statistical inference, comparisons of sizes and rates, and graphical displays of all kinds. We will make extensive use of media such as newspapers, magazines, articles on the Web, advertisements, letters to the editor, and policy statements of government officials to become active and critical consumers and presenters of data and argument. Throughout the semester each student will create an annotated notebook of current examples of fallacies, invalid arguments, misleading uses of data, and graphical distortions, along with critiques, and for some graphs, a corrected version. Computer software used: Excel. |
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1.00 units, Lecture
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| 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. |
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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 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 |
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1.00 units, Lecture
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| MATH 116 |
| Fair Division: Quantitative Approaches |
| Fair division problems involve the allocation of people, goods or power among the members of a group. This course will examine algorithms for allocating both divisible and indivisible assets, and, especially, the notion of fairness as a quantifiable property and as the subject of several important theorems. Theories will be illustrated by historical and contemporary examples, such as original quantitative arguments by Thomas Jefferson and Daniel Webster, a 1999 patent application for a division algorithm, the Law of the Sea Convention's regulations pertaining to sea-bed mining, and the mechanism of the U.S. Electoral College. Computer software tools will be MapInfo and Excel. This course does satisfy the Numerical and Symbolic Reasoning Requirement. |
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1.00 units, Lecture
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| MATH 116 |
| Mathematics of Equity |
| Mathematics of equity involves the allocation of people, goods, or power among the members of a group. This course examines algorithms for allocating both divisible and indivisible assets and, especially, the notion of fairness as a quantifiable property and as the subject of several important theorems. Topics include: the mathematics of voting, fair division and the mathematics of sharing, linear programming, and taxation. This course satisfies the numerical and symbolic reasoning requirement. |
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1.00 units, Lecture
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| 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 |
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1.00 units, Lecture
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| MATH 123 |
| Mathematical Pearls |
| An introduction to mathematical topics from logical thinking, sets, probability, geometry and art, and more. |
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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.
Prerequisite: A satisfactory score on the Mathematics Placement Exam |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| 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: Mathematics 125 with a grade of C- or better. |
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1.00 units, Lecture
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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 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 Mathmatics Placement Examination. |
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1.25 units, Lecture
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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.
Corequisite: Must be enrolled in Mathematics 131 concurrently. |
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0.25 units, Laboratory
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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.
Prerequisite: C- or better in Mathematics 126 or 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 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 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 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 Mathematics 131, or an appropriate score on the AP Examination or Trinity's Mathematics Qualifying Examination. |
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0.50 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. |
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1.00 units, Lecture
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| 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.. |
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1.00 units, Lecture
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| MATH 225 |
| Special Topics: Dynamical Systems & Chaos |
| This course will provide an introduction to the study of dynamics and chaos-that is, the study of how things change over time and whether or not such changes can be predicted in the long-term. Topics may include examples and applications ranging from discrete dynamical modeling in finance, the social sciences, and genetics, to continuous dynamical modeling, various physical phenomena, and fractal. Prerequisite: Mathematics 132 or 142. |
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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.
Prerequisite: C- or better in Mathematics 142 or Mathematics 132 or a 200-level Mathematics course, or permission of the 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.
Prerequisite: C- or better in Mathematics 132 or 142. |
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1.25 units, Lecture
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| 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. |
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1.00 units, Lecture
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| 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 the instructor. |
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1.00 units, Lecture
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| 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: Computer Science 115L and a C- or better in either Mathematics 132 or 142. |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| MATH 255 |
| Numerical Analysis |
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No Course Description Available.
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1.00 units, Lecture
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| MATH 257 |
| Intermediate Statistics for the Natural and Social Sciences |
A survey of statistical techniques and theories commonly used in the natural and social sciences. Topics may include sampling, non-parametric inference, analysis of variance, time series, tests of independence, linear models, or others as suggested by interests and backgrounds of the students.
Prerequisite: A suitable score on the Mathematics Placement Examination or a grade of C- or better in Mathematics 107.. |
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1.00 units, Lecture
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| 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.
A grade of C- or better in Mathematics 231 |
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1.00 units, Lecture
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| 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: Mathematics 305 with a grade of C- or better. |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| MATH 308 |
| Abstract Algebra II |
A continuation of Mathematics 307. Further topics from group, ring, and field theory.
Prerequisite: Mathematics 307 with a grade of C- or better. |
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1.00 units, Lecture
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| 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: Computer Science 115, either MATH 132 or MATH 142, and any mathematics course numbered 200 or higher. |
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1.00 units, Lecture
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| MATH 311 |
| Stochastic Processes |
| We explore some of the basic techniques used in the analysis of non-deterministic data. Topics may include the distribution of quadratic forms, the general linear model, diagnostic measures, model building, Markov chains, random walks, Poisson processes, and renewal theory. Prerequisite: Permission of the instructor. |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| 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 Mathematics 231. |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| MATH 325 |
| Special Topics in Continued Fractions |
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No Course Description Available.
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1.00 units, Lecture
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| MATH 325 |
| Special Topics in Algebra |
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No Course Description Available.
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1.00 units, Lecture
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| MATH 325 |
| Special Topics in Graph Theory |
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No Course Description Available.
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1.00 units, Lecture
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| MATH 325 |
| Special Topics in Geometry |
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No Course Description Available.
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| 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. |
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1.00 units, Lecture
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| MATH 332 |
| Analysis II |
Further topics which may include Fourier analysis, general integration theory, and complex analysis.
Prerequisite: C- or better in Mathematics 331. |
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1.00 units, Lecture
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| MATH 334 |
| Differential Equations |
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No Course Description Available.
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1.00 units, Lecture
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| 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.
A grade of C- or better in Mathematics 231 |
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1.00 units, Lecture
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| 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. |
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0.50 units min / 2.00 units max, Independent Study
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| MATH 400 |
| Senior Exercise |
| One of the most important equations in all of mathematics involves just five numbers. It relates these five numbers in such a fundamental fashion that a fair case can be made that these are the numbers on which hangs all of mathematics. Known as Euler’s equation, it is very simple:
eip + 1 = 0.
We are generally pretty comfortable with 1 and 0. But what about the others? What are they, and how does the relation among the five of them obtain?
The goal of the course is to investigate e, i, and p: to find out something of their history and their properties, and the relationship among them. This is a writing- and proof-intensive course. |
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1.00 units, Lecture
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| 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. |
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1.00 units, Independent Study
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| 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. |
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0.50 units, Independent Study
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| MATH 490 |
| Research Assistant |
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No Course Description Available.
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0.50 units min / 1.00 units max, Independent Study
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| MATH 497 |
| Senior Thesis |
| Required of, but not limited to, honors candidates. |
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1.00 units, Independent Study
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| MATH 498 |
| Senior Thesis Part I |
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No Course Description Available.
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2.00 units, Independent Study
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| MATH 499 |
| Senior Thesis Part 2 |
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No Course Description Available.
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2.00 units, Independent Study
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