Download e-book Introductory Analysis - A Deeper View of Calculus

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It ends with an introduction to the integral. This course contains a further study of integrals. It also includes an introduction to sequences and series of real numbers. Math and Math include topics covered in Math , Math , and Math The pace is faster then in the Math Math sequence, and topics are also covered in more depth. The study of matrices, vector spaces, and linear transformations. This is an important course for math majors and useful in many other disciplines and should be taken as soon after Calculus II as possible.

While one variable calculus i. It covers ideas and activities that reinforce interrelationships among topics in mathematics, especially as taught in secondary education. Themes that recur throughout the course are transformations, data analysis methods, and technology. This course satisfies the Writing in the Disciplines core requirement.

This course is primarily for non-majors, and should be skipped by most math majors. It covers a condensed version of the material in Math and Math This course is an introduction to proofs and the abstract approach that characterizes upper level mathematics courses. It serves as a transition into advanced mathematics, and should be taken after the initial calculus sequence and before or concurrently with mid-level mathematics courses.

The goal is to give students the skills and techniques that they will need as they study any type of advanced mathematics, whether it be in pure mathematics, applied mathematics, or application-oriented courses. In particular, this course covers topics that are ubiquitous throughout mathematics e.

A major objective of the course will be to teach students how to read, write, and understand proofs. Throughout the course students will be exposed to the notation, language, and methods used by mathematicians, and will gain practice using these in their own proofs.

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In addition, great emphasis is placed on writing and communication. This course is an introduction to Abstract Algebra, which is one of the major areas of mathematics. It focuses on the study of groups and rings, which are abstract objects used to generalize the operations of "addition" and "multiplication" from basic arithmetic. Proofs are used throughout the course.

Introduction to limits - Limits - Differential Calculus - Khan Academy

Abstract Algebra is one of the cornerstones of modern mathematics, and is used extensively in both pure and applied math. This course is required of all math majors. Differential equations are equations involving derivatives of a function. This course teaches methods for finding functions that are solutions to certain kinds of differential equations.

This particular course tends to be computational and uses many of the differentiation and integration techniques learned in Calculus I and II. Differential equations come up in many real-world applications of mathematics, and are useful in modeling. This is a great course for students interested in engineering, physical or biological sciences, economics, finance, or careers in industry. Real Analysis is a subject that takes a rigorous approach to the concepts studied in Calculus, such as convergence, limits of functions, continuity, differentiability, and integrability.

The rigorous approach involves a great deal of proofs, however the course is far more than simply "providing proofs of the things we learned in Calculus I and II". The new techniques developed through the rigorous approach allow methods for computing things that were inaccessible in Calculus I and II, and also provide qualitative and approximate results when precise ones are unavailable.

Real Analysis is one of the cornerstones of modern mathematics, and is used extensively in both pure and applied math. In addition, many advanced math classes at UH build off of the material in Math The material involves a mixture of proofs and computations. In many universities the material in Math and Math is combined into one course, but at UH it is done in two.


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The material of this course has significant overlap with the material in Math , and students should take one of Math or Math , but not both. Math majors who are not also double majoring in physics or engineering should take Math rather than Math This course is very similar to Math , but has more emphasis on the integration theorems for multivariable functions.

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It is primarily a service course for students majoring in physics and engineering, and it was developed as an alternate version of Math to cover integration theory in more detail so that these students can get a better mathematical background for the integration results required in such physics courses as electromagnetic field theory. Discrete mathematics is the study of mathematical structures that are isolated and discrete, rather than varying in a smooth or continuous way. In contrast to subjects such as calculus or real analysis, where the continuum of real numbers or smooth i.

While discrete mathematics is a subject studied by many mathematicians, this particular course at UH is primarily a service course for Computer Science students, and there is significant overlap with Math Transition to Advanced Mathematics. Math majors should not take this course, and should instead take Math Spivak makes his writing on the main objective of the book — Stokes Theorem — painless and easy to grasp.

Readers are encouraged to keep a pen and paper on hand to rewrite the proofs on their own. Review : In this uniquely interesting book, photographer Mariana Cook offers readers high quality black and white photographs of 92 noteworthy mathematicians. However it provides a much needed break from the rather austere climate that the math world is usually comprised of. Her selected mathematicians come from diverse backgrounds and have all reached their authoritative status in equally different ways.

Each photograph is accompanied by a quick, informative and often enlightening essay by the mathematician at hand, frequently revealing the passion and deep love for their discipline that each mathematician possesses. Cook does a wonderful job of capturing her subjects in an honest and purely human light.

As such, this title is the ideal coffee table book for math geeks. Review : In Sacred Mathematics, Hidetoshi and Rothman present a tantalizing and detailed history of Sangaku puzzles that will keep the reader engaged for many hours.

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For those who are unfamiliar with the subject, sangakus are Japanese geometrical puzzles that were created on wooden tablets and hung in sacred temples and shrines. Readers will discover how the Japanese cleverly intertwined the mathematical, the spiritual, and the artistic to create their own cultural brand of geometry. Sangaku was formulated during an era before western influence had reached Japan. This makes it a unique and fascinating art that has attracted many mathematicians.

This hardcover volume is rich of illustrations and would be a nice coffee table book. Review : Math undergrads will find Principles and Techniques in Combinatorics to be a detailed but easy to read book. This is a much needed textbook that can truly be classified as introductory.