Transition to Higher Mathematics

Transition to Higher Mathematics
Author: Bob A. Dumas
Publisher: McGraw-Hill Education
Total Pages: 0
Release: 2007
Genre: Logic, Symbolic and mathematical
ISBN: 9780071106474

This book is written for students who have taken calculus and want to learn what "real mathematics" is.

A Gateway to Higher Mathematics

A Gateway to Higher Mathematics
Author: Jason H. Goodfriend
Publisher: Jones & Bartlett Learning
Total Pages: 346
Release: 2005
Genre: Computers
ISBN: 9780763727338

A Gateway to Higher Mathematics integrates the process of teaching students how to do proofs into the framework of displaying the development of the real number system. The text eases the students into learning how to construct proofs, while preparing students how to cope with the type of proofs encountered in the higher-level courses of abstract algebra, analysis, and number theory. After using this text, the students will not only know how to read and construct proofs, they will understand much about the basic building blocks of mathematics. The text is designed so that the professor can choose the topics to be emphasized, while leaving the remainder as a reference for the students.

Towards Higher Mathematics: A Companion

Towards Higher Mathematics: A Companion
Author: Richard Earl
Publisher: Cambridge University Press
Total Pages: 545
Release: 2017-09-07
Genre: Mathematics
ISBN: 1107162386

This book allows students to stretch their mathematical abilities and bridges the gap between school and university.

An Accompaniment to Higher Mathematics

An Accompaniment to Higher Mathematics
Author: George R. Exner
Publisher: Springer Science & Business Media
Total Pages: 232
Release: 1999-06-22
Genre: Mathematics
ISBN: 9780387946177

Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.

A Bridge to Higher Mathematics

A Bridge to Higher Mathematics
Author: Valentin Deaconu
Publisher: CRC Press
Total Pages: 213
Release: 2016-12-19
Genre: Mathematics
ISBN: 1498775276

A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof. For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn’s lemma and the axiom of choice are included. More challenging problems are marked with a star. All these materials are optional, depending on the instructor and the goals of the course.

Bridge to Higher Mathematics

Bridge to Higher Mathematics
Author: Sam Vandervelde
Publisher: Lulu.com
Total Pages: 258
Release: 2010
Genre: Education
ISBN: 055750337X

This engaging math textbook is designed to equip students who have completed a standard high school math curriculum with the tools and techniques that they will need to succeed in upper level math courses. Topics covered include logic and set theory, proof techniques, number theory, counting, induction, relations, functions, and cardinality.

A Transition to Advanced Mathematics

A Transition to Advanced Mathematics
Author: William Johnston
Publisher: Oxford University Press
Total Pages: 766
Release: 2009-07-27
Genre: Mathematics
ISBN: 0199718660

A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.

Pearson Edexcel GCSE (9-1) Mathematics Higher Student Book 1

Pearson Edexcel GCSE (9-1) Mathematics Higher Student Book 1
Author: Katherine Pate
Publisher: Pearson Education
Total Pages: 416
Release: 2020-06-11
Genre: Mathematics
ISBN: 1292346124

The new edition of Pearson Edexcel GCSE (9-1) Mathematics Higher Student Book 1 develops reasoning, fluency and problem-solving to boost students’ confidence and give them the best preparation for GCSE study. Purposefully updated based on feedback from thousands of teachers and students, as well as academic research and impact studies Bolsters preparation for GCSE with new questions that reflect the latest exams and a format that seamlessly aligns with our GCSE Maths courses Shown to help GCSE students master maths with confidence with a UK-specific approach that draws upon global best practices and cutting-edge research Tried-and-tested differentiation with a unique unit structure and improved pacing to support every student’s progress Extra skills-building support, problem-solving, and meaningful practice to consolidate learning and deepen understanding New additions to boost progression and post-GCSE study such as ‘Future skills questions’ and ‘Working towards A level’ features

Higher Mathematics for Physics and Engineering

Higher Mathematics for Physics and Engineering
Author: Hiroyuki Shima
Publisher: Springer Science & Business Media
Total Pages: 693
Release: 2010-04-12
Genre: Science
ISBN: 3540878645

Due to the rapid expansion of the frontiers of physics and engineering, the demand for higher-level mathematics is increasing yearly. This book is designed to provide accessible knowledge of higher-level mathematics demanded in contemporary physics and engineering. Rigorous mathematical structures of important subjects in these fields are fully covered, which will be helpful for readers to become acquainted with certain abstract mathematical concepts. The selected topics are: - Real analysis, Complex analysis, Functional analysis, Lebesgue integration theory, Fourier analysis, Laplace analysis, Wavelet analysis, Differential equations, and Tensor analysis. This book is essentially self-contained, and assumes only standard undergraduate preparation such as elementary calculus and linear algebra. It is thus well suited for graduate students in physics and engineering who are interested in theoretical backgrounds of their own fields. Further, it will also be useful for mathematics students who want to understand how certain abstract concepts in mathematics are applied in a practical situation. The readers will not only acquire basic knowledge toward higher-level mathematics, but also imbibe mathematical skills necessary for contemporary studies of their own fields.