MAT - Introduction to Calculus. MAT - Calculus A. MAT - Calculus B. MAT - Calculus C. MAT - Calculus I. MAT - Intro. MAT - Vector Geometry. MAT - Linear Algebra. MAT - Number Theory. MAT - Abstract Algebra. MAT - Foundations of Analysis. MAT - Introduction to Analysis. MAT - Real Analysis. MAT - History of Mathematics. MAT - Geometric Structures. MAT - Topology and Geometry.
MAT - Seminar in Mathematics. MAE - Micro-Teaching.
MAE - Clinical Experience. MAT - Algebra for Teachers.
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MAT - Geometry for Teachers. MAT - Algebra I. The aesthetic and structural properties of these structures will be described following a chronological line. Whenever the opportunity presents itself, this discussion will be informed by basic modern mathematics such as geometry, trigonometry, and calculus. Calculus A emphasizes the process of problem solving and application of calculus to the natural sciences, and requires students to think deeper about the concepts covered.
Students will acquire basic skills needed for a quantitative approach to scientific problems. The course introduces the mathematics needed to study change in a quantity. Topics include functions, limits, continuity, rate of change of functions, integrals, graphing and their applications. Calculus B emphasizes the process of problem solving and application of calculus to the natural sciences, and requires students to think deeper about the concepts covered.
Students will acquire basic skills needed for quantitative approach to scientific problems. Topics include integration techniques, application of integrals to physics, geometry and ecology, solution of differential equations and their applications, and Taylor series. The flow is historical, but the emphasis is on doing the mathematics in a pedagogically effective way. This means that the material is developed from within the relevant context: that of the contributions of Greek thinkers, Copernicus, Galileo, Kepler, Descartes, Newton and Leibniz.
But, it also means that the notation is modern and that the material is selected so as to cover the basics of the subject. Calculus is developed by fusing essential insights of both Leibniz and Newton together into a complete "short calculus". This starts from scratch, is free of most theoretical "baggage", and concentrates on the intuitive grasp of the basic elements.
What will have emerged is a basic mathematics course that is surrounded by the important scientific concerns of the times. A quick overview of conventional differential calculus follows next as preparation for a detailed look at polar coordinates, polar functions, and polar calculus. The course concludes with the application of polar calculus to planetary motion. Topics include sets, functions, limits, continuity, derivatives, integrals, and applications.
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Also covered are transcendental functions and their inverses, infinite sequences and series, parameterized curves in the plane, and polar coordinates. Aimed at highly engaged math students, Honors Calculus emphasizes the 'why' of mathematics as well as the 'how'. Specifically, it begins with a thorough introduction to mathematical reasoning and proofs and then proceeds to carefully develop the central topics limits, differentiation, integration of one variable Calculus.
Whether you have had Calculus before or not, this course will challenge you in new ways. It will strongly enhance your critical thinking skills and provide you with a much more solid grounding for any future mathematics courses. Honors calculus courses are required for the honors math major, but they have much to offer for mathematically inclined students of all majors. Math majors with AP credit for Calculus 1 and 2 may count Honors Calculus 1 and 2 in place of the upper level math courses Introduction to Mathematical Reasoning and Real Analysis A rigorous course in differential and integral calculus of one variable.
Topics include an axiomatic formulation of the real numbers, mathematical induction, infima and suprema, functions, continuity, derivatives, integrals, infinite sequences and series, transcendental functions and their inverses, and applications. The course stresses careful mathematical definitions and emphasizes the proofs of the standard theorems of the subject.
Tutorial for the second course of the two-semester Calculus sequence for Life and Social science majors. MATH Honors Mathematics Tutorial. It aspires to present the first year students with an opportunity to participate in the excitement of discovering ideas of their own by practicing the mathematical way of thinking.
This topical course will be rich, in content and context. It will stress the connections between mathematics and modern society by considering a wide variety of problems ranging from environmental and economic issues to social and political situations that can be modeled and solved by mathematical means.
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Also, by giving appropriate assignments and projects, it will allow students to make contributions in areas of their interest and expertise. This is a second-semester calculus course designed for biology and social science majors. It is required for all premedical students. Mathematics plays a prominent role in the understanding of complex systems in modern biology and social science.
This course aims to develop basic mathematical literacy in students for this modern era. Students will acquire skills needed for a quantitative approach to scientific problems and the mathematics needed to study change in a quantity. Topics include integration techniques, solution of differential equations, geometric series, Taylor series and their applications to physics, geometry and ecology.
Pre-requisites: First semester calculus or freshmen calculus. Note: this course is delivered fully online. The course design combines required live weekly meetings online with self-scheduled lectures, problems, assignments, and interactive learning materials. To participate, students will need to have a computer with webcam, reliable internet connection, and a quiet place to participate in live sessions.
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Students who will be on the Main campus or residing in the Michiana region may only enroll with permission from the DUS of the Department of Mathematics. The course serves as a gateway to more advance mathematical methods that are commonly used in contemporary scientific studies and their literature.
Students will learn how to take a mathematical approach to various scientific problems, solve the resulting equations, and interpret the mathematical solution in the original context. There will be course projects and some usage of computing software. Topics include matrix algebra, eigenvalues and eigenvectors, vector-valued functions, linear and non-linear systems of differential equations, and phase portraits.
Topics include space curves, surfaces, functions of several variables, partial derivatives, multiple integrals, line integrals, surface integrals, Stokes theorem, and applications.
Weekly tutorial sessions. Cross-listed with PHYS Topics include elementary matrices, LU factorization, QR factorization, the matrix of a linear transformation, change of basis, eigenvalues and eigenvectors, solving first-order differential equations and second-order linear differential equations, and initial value problems.
This course is part of a two-course sequence that continues with Math Credit is not given for both Math and Math An introduction to vector spaces, matrices, linear transformations, inner products, determinants and eigenvalues. Emphasis is given to careful mathematical definitions and understanding the basic theorems of the subject. The general subject is numbers of all sorts—integers, rationals, real numbers, etc. The main point will be to treat everything the way a mathematician would.
That is, we will give precise definitions of the objects we consider and careful statements of the assertions we make about them. And, most importantly, we will justify our assertions by giving mathematical proofs. Topics covered include basic language of sets, common methods of proof, integers, factorization, modular arithmetic, rational numbers, completeness, real numbers, cardinality, limits, and continuity.
Topics include first-order equations, n-th order linear equations, power series methods, systems of first order linear equations, non-linear systems and stability. Topics covered include algebra and geometry of vectors and linear transformations; continuity, differentiation and integration for functions of several variables; and various applications of all these things.
Material will be covered in substantially greater depth than in similar courses e.