| 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 |
| 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 103 |
| Earth Algebra: Modeling Our Environment |
| This course offers students an opportunity to strengthen their numerical and algebraic reasoning abilities. Linear, quadratic, exponential, and rational models will be studied as they apply to current environmental issues, such as global warming and epidemiology. 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 104 |
| Hartford Current Issues: Logic in the Media |
| This course offers students an opportunity to strengthen their numerical and logical reasoning abilities. The concepts and techniques of logic will be applied to quantitative and verbal arguments from current local and national news sources and advertisements. Three hours of lecture per week for half of the semester. |
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0.50 units, Lecture
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| MATH 105 |
| Visual Geometry: Mathematics of Patterns |
| This course will examine the mathematical underpinnings of patterns from diverse cultures and times, ranging from Egyptian tom decorations to medieval church pavement and from Nigerian fabric designs to the tiling of the Alhambra. In the process, we will explore the evolution of the definition and mathematical properties of symmetry from the incorporation in the Platonic solids of ancient Greece and the semi-regular tilings studied by Kepler to the more sophisticated patterns found in today's Penrose tilings and quasicrystals. |
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1.00 units, Lecture
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| MATH 105 |
| Visual Geometry: Math in Art and Architecture |
| This course will examine mathematics as it appears in art and architecture. Topics will include geometric compass and straight-edge constructions, the use of special proportions in Renaissance buildings, the symmetries of architectural ornament, the Platonic solids, and the projective geometry behind perspective and its later conscious distortion in painting. |
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1.00 units, Lecture
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| ECON 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. Students having a mathematical background which includes Mathematics 231 should consider the Mathematics 305, 306 sequence for work in probability and statistics. Prerequisite: Two years of high school algebra. |
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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. Students having a mathematical background which includes Mathematics 231 should consider the Mathematics 305, 306 sequence for work in probability and statistics. |
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1.00 units, Lecture
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| COLL 114 |
| Judgment & Decision Making |
| Most of the decisions that you make in your lifetime require very little thought. Occasionally, however, you will encounter a situation that requires careful and systematic analysis. This course examines the basic issues in formal decision-making. The notions of utility and risk will be introduced, and quantitative techniques used in the decision-making process will be developed. Examples will be drawn from medicine, law, foreign policy, economics, psychology, sports and gambling. |
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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. |
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1.00 units, Lecture
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| MATH 115 |
| Visual Geometry: Math in Art and Architecture |
| This course will examine mathematics as it appears in art and architecture. Topics will include geometric compass and straight-edge constructions, the use of special proportions in Renaissance buildings, the symmetries of architectural ornament, the Platonic solids, and the projective geometry behind perspective and its later conscious distortion in painting. |
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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. |
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1.00 units, Lecture
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| MATH 123 |
| Visual Geometry: Math in Art and Architecture |
| This course will examine mathematics as it appears in art and architecture. Topics will include geometric compass and straight-edge constructions, the use of special proportions in Renaissance buildings, the symmetries of architectural ornament, the Platonic solids, and the projective geometry behind perspective and its later conscious distortion in painting. |
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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. |
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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”). |
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1.50 units, Lecture
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| MATH 132 |
| Calculus II |
Topics concerning the Riemann integral and its applications, techniques of integration, first-order ordinary differential equations, and sequences and series.
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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1.50 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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1.50 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. |
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1.00 units, Lecture
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| MATH 219 |
| Theory of Computation |
A selection of topics intended to serve as an introduction to formal languages and automata theory. The topics will be chosen from among finite state machines, pushdown automata, Turing machines, the Chomsky language hierarchy and related questions of computability. Prerequisites: Computer Science 115L and either Mathematics 205 or Computer Science 203. Offered in alternate years.
Prerequisite: C- or better in Computer Science 115L and either Computer Science 203 or Mathematics 205. |
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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 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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1.50 units, Lecture
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| MATH 232 |
| Calculus IV Adv Topics |
The calculus of vector-valued functions, including Green's and Stokes's theorems, l'Hopital's rule and indeterminate forms, improper integrals, and sequences and series. Prerequisite: Grade of C- or better in Mathematics 231.
Prerequisite: C- or better in Mathematics 132. |
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1.00 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. |
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1.00 units, Lecture
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| MATH 303 |
| The Mathematics of Discrete Structures |
A broad introduction to, and exploration of, modern algebra. Examples of algebraic structures may be drawn from among the following areas: symmetry, number theory, solutions to equations, modular arithmetic, permutations, matrices, and wallpaper patterns. This course may not be repeated for credit. Students with credit for Mathematics 307 are not normally eligible to receive credit for this course.
Prerequisite: C- or better in Mathematics 228, or permission of the instructor. |
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1.00 units, Lecture
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| MATH 304 |
| The Mathematics of Continuous Structures |
We will develop tools from calculus and analysis in order to study a variety of continuous structures: mathematical objects which embody in different ways the notions of limit and continuity. Equal emphasis will be placed on proving and applying analytical tools. This is not a survey course. Rather, one or two topics will be explored in detail. Such topics may include sequences and series, Fourier series and differential equations, dynamical systems, special functions, approximation theory, analytic theory of continued fractions, integration theory, and complex analysis. Students with credit for Mathematics 331 are not normally eligible to receive credit for this course.
Prerequisite: C- or better in Mathematics 132. |
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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.
Prerequisite: C- or better in Mathematics 132. |
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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 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 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 |
| 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 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. |
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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.
Prerequisite: C- or better in Mathematics 132. |
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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 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 |
| Thesis |
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No Course Description Available.
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1.00 units, Independent Study
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| MATH 812 |
| Graph Theory with Applications |
Introduction to the theory of graphs, with applications to real world problems. Topics will 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, colorability, 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 and Computer Science 115. |
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1.00 units, Lecture
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| MATH 813 |
| Combinatorics & Computng |
Introduction to combinatorics and use of the computer to carry out computations involving discrete mathematical structures. 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, matrix methods. Prerequisite: Mathematics 228 with a grade of C- or higher. 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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