# A Second Course on Real Functions

## Mathematics

MATH - Linear Algebra I A course intended to introduce students to elementary linear algebra, particularly at a computational and applied level. Topics include matrices and systems of equations, inversion, determinants, vectors, inner products, eigenvectors and eigenvalues. Attention will be given to the history of cryptology and the public-policy questions raised by its use in conjunction with the Internet. However, the focus will be on the mathematical tools needed to develop and analyze encryption algorithms.

MATH - Introductory Finite Mathematics II Elementary linear programming, counting methods involving permutations and combinations, probability, statistics, regression, and consumer mathematics including interest calculations, annuities and amortizations. MATH - Vector Calculus A study of vector functions and functions of several variables and their derivatives; Applied maximum and minimum problems, Lagrange multipliers, multiple integration, integration in polar, cylindrical and spherical coordinates; Green's, Stokes' and the Divergence Theorem.

Specific topics include bonds, securities, analysis of risk and basic principles of pricing theory. MATH - Introduction to Proofs and Problem Solving An introductory course intended to familiarize students with mathematical reasoning and proof techniques, including direct reasoning, indirect reasoning, and mathematical induction. Topics include elementary number theory, logic, sets, functions, and relations.

There will be some emphasis on proofs. Topics include matrices, abstract vector spaces, subspaces, bases, inner product spaces, linear transformations, matrix factorizations, symmetric matrices, quadratic forms, and applications of linear algebra. Topics include number systems and an introduction to groups, and some other mathematical structures. Topics include the postulates and theorems of both classical and modern Euclidean geometry. MATH - Introduction to Probability Basic notions of probability; discrete and continuous random variables; expectation; moment generating functions; joint discrete random variables.

MATH - Methods of Numerical Analysis Number systems and errors, solutions of polynomial and other nonlinear equations, interpolation, numerical differentiation and integration, the cubic spline. Natural numbers. Finite and infinite sets, ordinals and cardinals.

## A Second Course On Real Functions

Recursion theorems. Arithmetic of cardinals and ordinals. A brief introduction to set-theoretic topology. Construction of the real numbers and basic properties. Axiomatically built theories and their models. Detailed study of one or more simple mathematical theories. Recursive functions. Basic ideas of automated theorem proving. MATH - Introductory Mathematical Analysis Cardinality, real numbers and their topology, sequences, limits, continuity, and differentiation for functions of one real variable.

Students considering a degree in Mathematics with Honours are encouraged to complete this course by the end of their second year.

### Outline syllabus

Topics may include mathematics of ancient cultures, cultural aspects of mathematics, how mathematics developed around the world, famous mathematicians and classical mathematics texts. This course is designed for majors in mathematics or mathematics education with a solid background in mathematics. It will be offered in the winter semester, alternating with MATH MATH - Topics in Modern Mathematics A survey of modern mathematics, examining the objectives of mathematical advancement, important modern results in mathematics, mathematicians of the modern era, and the influences of modern mathematics on contemporary science.

The focus of this course will be on mathematics after Gauss post The emphasis will be on general modern approaches to mathematical problems and the philosophy of mathematics, rather than specific results. Topics will include but are not limited to : the nature of mathematical knowledge, origins of modern mathematics, biographies of mathematicians and the influence of mathematics on contemporary science.

## A Second Course in Complex Analysis | Mathematical Association of America

MATH - Complex Analysis I Complex numbers, analytic functions, contour integration, Cauchy's theorem, infinite series, calculus of residues, basic theory of conformal mappings. MATH - Mathematical Analysis II The Riemann integral for functions of one variable, sequences and series of functions, differentiation and integration for functions of several variables.

MATH - Real Analysis I Construction of the real numbers, structure of metric spaces, continuous functions on metric spaces, convergence of series, differential equations. Topics include divisibility, primes, congruences, number theoretic functions, and diophantine equations. MATH - Matrix Theory Topics include: positive definiteness, Jordan canonical form, nonnegative matrices, and applications in matrix analysis. Topics include permutations and combinations, inclusion and exclusion, generating functions, and a brief introduction to graph theory. MATH - Linear and Discrete Optimization A course in the theory and techniques of linear programming; convexity and extreme points of polyhedral sets, the simplex method, duality and selected applications will be covered.

MATH - Non-Euclidean Geometry This course gives an explaination of the nature and foundations of geometry and uses for this purpose the systems of non-Euclidean geometry.

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- A.C.M. van Rooij (Author of Non Archimedean Functional Analysis).
- Mathematics;
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- A Second Course on Real Functions.

This book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable. Numerous exercises are included throughout, offering ample opportunities to master topics by progressing from routine to difficult problems.

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Hints or solutions to many of the more challenging exercises make this book ideal for independent study, or further reading. Intended as a sequel to a course in single variable analysis, this book builds upon and expands these ideas into higher dimensions. The modular organization makes this text adaptable for either a semester or year-long introductory course. Topics include: differentiation and integration of functions of several variables; infinite numerical series; sequences and series of functions; and applications to other areas of mathematics.

Many historical notes are given and there is an emphasis on conceptual understanding and context, be it within mathematics itself or more broadly in applications, such as physics. Vera T. This volume will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Mathematics Analysis.

Undergraduate Texts in Mathematics Free Preview.