Towards Higher Mathematics A Companion
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Towards Higher Mathematics A Companion
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Author : Richard Earl
language : en
Publisher: Cambridge University Press
Release Date : 2017-09-07
Towards Higher Mathematics A Companion written by Richard Earl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-07 with Mathematics categories.
This book allows students to stretch their mathematical abilities and bridges the gap between school and university.
Elements Of Higher Mathematics
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Author : Frans Keune
language : en
Publisher: Radboud University Press
Release Date : 2024-10-29
Elements Of Higher Mathematics written by Frans Keune and has been published by Radboud University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-29 with Mathematics categories.
This is a textbook for beginning mathematics students. Knowledge of school mathematics is not presumed: it starts with the basics of counting. The underlying idea is that the best way to learn mathematics is by doing mathematics. For beginning students it is sometimes a problem to assume when looking for proof. For the exercises in this textbook, this situation does not occur: except for the introductory part all is built on Peano's axioms for the natural numbers, using the language of set theory only. The book starts explaining the way mathematics works: the use of intuitive set theory and the relation between language and mathematical entities. The common thread in the book is the construction of the number system all the way from the natural numbers, via the rationals and the reals to the complex numbers. For the student, the advantages of this approach are: - One learns concepts which are fundamental for all of mathematics. - The common thread offers a natural way for the introduction of these concepts. It helps to stay motivated during the course. - One learns to think like a mathematician. - One obtains insight into the way mathematics is built from simple ideas. - It helps to decide whether one is fitted for a mathematics study. For the interested reader also the other possible completions of the rationals - the p-adic numbers - are constructed. The book contains more than just the construction of the number system: there is also attention for its use, especially in combinatorics, number theory and cryptography, leaving mathematical analysis to the many textbooks for analysis and calculus courses.
Statistics For Higher Mathematics
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Author : Ralph Riddiough
language : en
Publisher: Nelson Thornes
Release Date : 1998
Statistics For Higher Mathematics written by Ralph Riddiough and has been published by Nelson Thornes this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Juvenile Nonfiction categories.
Full coverage of the Statistics unit is provided in a separate book which covers everything your students need for this option.
A Bridge To Higher Mathematics
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Author : Valentin Deaconu
language : en
Publisher: CRC Press
Release Date : 2016-12-19
A Bridge To Higher Mathematics written by Valentin Deaconu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-19 with Mathematics categories.
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.
Why Study Mathematics
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Author : Vicky Neale
language : en
Publisher: London Publishing Partnership
Release Date : 2020-10-27
Why Study Mathematics written by Vicky Neale and has been published by London Publishing Partnership this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-27 with Mathematics categories.
Considering studying mathematics at university? Wondering whether a mathematics degree will get you a good job, and what you might earn? Want to know what it's actually like to study mathematics at degree level? This book tells you what you need to know. Studying any subject at degree level is an investment in the future that involves significant cost. Now more than ever, students and their parents need to weigh up the potential benefits of university courses. That's where the Why Study series comes in. This series of books, aimed at students, parents and teachers, explains in practical terms the range and scope of an academic subject at university level and where it can lead in terms of careers or further study. Each book sets out to enthuse the reader about its subject and answer the crucial questions that a college prospectus does not.
The Concise Oxford Dictionary Of Mathematics
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Author : Richard Earl
language : en
Publisher: Oxford University Press
Release Date : 2021-07-29
The Concise Oxford Dictionary Of Mathematics written by Richard Earl and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-29 with Mathematics categories.
With over 4,000 entries, this informative A to Z provides clear, jargon-free definitions on a wide variety of mathematical terms. Its entries cover both pure and applied mathematics, and include key theories, concepts, methods, programmes, people, and terminology. For this sixth edition, around 800 new terms have been defined, expanding on the dictionary's coverage of topics such as algebra, differential geometry, algebraic geometry, representation theory, and statistics. Among this new material are articles such as cardinal arithmetic, first fundamental form, Lagrange's theorem, Navier-Stokes equations, potential, and splitting field. The existing entries have also been revised and updated to account for developments in the field. Numerous supplementary features complement the text, including detailed appendices on basic algebra, areas and volumes, trigonometric formulae, and Roman numerals. Newly added to these sections is a historical timeline of significant mathematicians lives and the emergence of key theorems. There are also illustrations, graphs, and charts throughout the text, as well as useful web links to provide access to further reading.
Bridge To Higher Mathematics
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Author : Sam Vandervelde
language : en
Publisher: Lulu.com
Release Date : 2010
Bridge To Higher Mathematics written by Sam Vandervelde and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Education categories.
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.
An Accompaniment To Higher Mathematics
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Author : George R. Exner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Accompaniment To Higher Mathematics written by George R. Exner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For Students Congratulations! You are about to take a course in mathematical proof. If you are nervous about the whole thing, this book is for you (if not, please read the second and third paragraphs in the introduction for professors following this, so you won't feel left out). The rumors are true; a first course in proof may be very hard because you will have to do three things that are probably new to you: 1. Read mathematics independently. 2. Understand proofs on your own. :1. Discover and write your own proofs. This book is all about what to do if this list is threatening because you "never read your calculus book" or "can't do proofs. " Here's the good news: you must be good at mathematics or you wouldn't have gotten this far. Here's the bad news: what worked before may not work this time. Success may lie in improving or discarding many habits that were good enough once but aren't now. Let's see how we've gotten to a point at which someone could dare to imply that you have bad habits. l The typical elementary and high school mathematics education in the United States tends to teach students to have ineffective learning habits, 1 In the first paragraph, yet. xiv Introduction and we blush to admit college can be just as bad.
Towards Higher Categories
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Author : John C. Baez
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-24
Towards Higher Categories written by John C. Baez and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-24 with Algebra categories.
The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics
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Author : Douglas Cenzer
language : en
Publisher: World Scientific
Release Date : 2022-01-27
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics written by Douglas Cenzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-27 with Mathematics categories.
This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Gödel's Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy.