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Course Criteria
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4.00 Credits
This course studies the calculus in more than one dimension. Topics include partial derivatives, multiple integrals, and the major theorems of Green, Gauss, and Stokes. NOTE: Either MTH 164 or MTH 163 can be taken after MTH 162 or MTH 143. The usual procedure would be to take MTH 164 followed by MTH 163. Usually MTH 164 is taken first since its subject matter is more closely related to MTH 162. However, some engineering majors require MTH 163 (Differential Equations) to be completed by the end of the fall semester of the sophomore year.
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4.00 Credits
An introduction to the basic concepts of linear algebra: matrices, determinants, vector spaces and linear transformations, as well as to ordinary differential equations with an emphasis on linear differential equations, second order equations with constant coefficients and systems of differential equations. Applications to physical, engineering and life sciences. This course differs from MTH 163 in that it has more material on linear algebra (including a discussion of eigenvalues), and the only differential equations covered are linear ones with constant coefficients, along with systems thereof. For many students, taking MTH 165 will eliminate the need to take MTH 235 (linear algebra). Topics covered: elementary methods, linear equations, and systems with constant coefficients, solutions in series, special functions, phase plane analysis and stability, Laplace transform, extremal problems.
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5.00 Credits
This is the second semester of the honors calculus sequence, covering the material from MTH 161, MTH 162, MTH 163, and MTH 164 in greater depth from the standpoint of both theory and application.
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5.00 Credits
This is the last semester of the honors sequence of MTH 171, MTH 172, MTH 173, and MTH 174.
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4.00 Credits
Introduces some of the basic techniques and methods of proof used in mathematics and computer science. Methods of logical reasoning, mathematical induction, relations, functions, and more. The course also contains some applications of these techniques. The course concludes with an application of the techniques learned to either group theory or real analysis.
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4.00 Credits
Theory and applications of random processes, including Markov chains, Poisson processes, birth-and-death processes, random walks.
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4.00 Credits
Discrete and continuous probability distributions and their properties. Principle of statistical estimation and inference. Point and interval estimation. Maximum likelihood method for estimation and inference. Tests of hypotheses and confidence intervals, contingency tables, and related topics.
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4.00 Credits
Basics of Brownian motion, Ito integrals and stochastic differential equations at a level of rigor appropriate for undergraduates. We will apply this to the Black-Scholes formula for pricing European call options.
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4.00 Credits
Aimed at building problem-solving ability in students through the development of mathematical models for certain real-life situations in the biological sciences. Topics are selected from epidemiology, population growth, genetics and demographics amongst other things. Both discrete and continuous models as well as both deterministic and stochastic ones are treated. Models treated cover a variety of phenomena both discrete and continuous, linear and non-linear, determinstic and stochastic. Some topics that might be treated are Leslie Matrices in Demographics, Exponential and Logistic growth,Gompertz growth in tumors, Hardy-Weinberg Law in population genetics, Lotka-Volterra predator-prey systems, principle of competitive exclusion,the Kermack-McKendrick model of epidemics (and variants), Markov chain models (with the requisite intro to probability) and the stochastic pure birth process and epidemic models.
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4.00 Credits
Divisibility, primes, congruences, pseudo primes. Classical, public-key and knapsack ciphers. Other topics in number theory and applications to computer sciences as time permits.
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