![]() Mathematics 3321 or consent of instructor. Topics include divisibility and primes,Ĭongruences, Eulers theorem, primitive roots, and quadratic reciprocity. A study of the properties of the integers. Sampling, tests of hypotheses, estimation, linear models, and regression. Axioms and basic properties, random variables, univariate probability functions andĭensity functions, moments, standard distributions, law of large numbers, and central Mathematics 1411 or consent of instructor. Of higher order, Laplace transforms, systems of differential equations. First order equations, existence and uniqueness of solutions, differential equations The history of the development of mathematics, the lives and ideas of noted mathematicians. Limit points, convergent sequences, compact sets, connected sets, dense sets, nowhereĭense sets, separable sets. Prerequisite: Mathematics 1411 or consent of instructor.ģ321. ![]() A systematic development of topics selected from metric and nonmetric geometries,Ĭomparison of postulate systems. Linear equations, matrices, determinants, vector spaces, and linear transformations.Īpplications to the sciences and economics are included. Geometry of R 2 and R 3 including the dot product and parametric equations of lines and planes. Prerequisite: MAT 1404 or consent of instructor. ProblemsĪre drawn from many different fields of mathematics, yet very accessible to any student Have broad application for creatively thinking through many sorts of problems. Emphasis is on problems from competitions, but the techniques Problem Solving. This course presents many problem-solving techniques not typically found in other Problems given are often open-ended and may lack a published solution Is on generating ideas for solving problems and then testing those ideas to see if Junior Workshop. This course is designed to improve the student's ability to "do math at the board"Īnd to encourage a willingness to engage mathematical problems creatively. Each student is expected to write a paper and present a talk based on it inĪddition to fulfilling the other requirements. This course is similar to 2107 except that extra work is required to earn junior-levelĬredit. Grade of C (2.0) or better in Mathematics 1411, or satisfactory placement. Vectors, vector calculus, functions of several variables, multiple integrals. Prerequisite: Successful demonstration ofĢ412. A significantĪmount of instruction is computer-based. Testing, inference, and estimation, using the logical methods of mathematics. The superstructure of statistical methodology, including hypothesis Emphasis on a deep understanding of the fundamentalĮlements of so-called "statistical thinking", including randomness, uncertainty, modeling,Īnd decision processes. Statistics may be broadly defined as the science of making rational decisions in ![]() Of computer science, and a development of the imagination and analytical skills required Introduction to the mathematical foundation of computer science with two co-equalĬomponents: a study of combinatorics and graph theory including topics from the theory Public announcements of speakers will be made. Oral presentationsĪre selected for their interest and accessibility. Not normally seen in the first two years of undergraduate studies. A forum for exposing students to the rich and deep areas of mathematics and its applications Grade of C (2.0) or better in Mathematics 1404, or satisfactory placement. L'Hopitals Rule, inverse trigonometric and hyperbolic functions, methods of integration,Īnalytic geometry, applications of integrals, sequences and series. Prerequisite: Grade of C (2.0) or better in Mathematics 1303, or satisfactoryġ411. Limits, derivatives, applications of derivatives, integration, logarithmic and exponentialįunctions. Polynomials functions trigonometry on the unit circle parametric and polar coordinates Ĭonic sections arithmetic and geometric sequences math induction. Advanced algebra and trigonometry needed for Calculus. Prove a significant number of theorems on their own. Historical perspective and philosophical implications are included. The axiomatic method and consistency, independence and completeness of axiom systems. Neutral geometry hyperbolic geometry (non-Euclidean geometry of Gauss, Bolyai, Lobachevsky) ![]() Study of Euclid's geometry Hilbert's axioms To use language precisely and efficiently. On the students strengthening of his or her imagination, deductive powers, and ability Development of the mathematical way of thinking through firsthand experience.
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