Search Results: proof-core-books-in-advanced-mathematics


Author: C. Plumpton,R. L. Perry,E. Shipton

Publisher: Macmillan International Higher Education

ISBN: 1349071994

Category: Logic, Symbolic and mathematical

Page: 88

View: 6452

A Logical Introduction to Proof

Author: Daniel Cunningham

Publisher: Springer Science & Business Media

ISBN: 1461436303

Category: Mathematics

Page: 356

View: 614

The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.

Examinations in Mathematics

Author: N.A

Publisher: Macmillan International Higher Education

ISBN: 1349080896


Page: 197

View: 2455

A Level Further Mathematics for OCR A Pure Core Student Book 1 (AS/Year 1)

Author: Vesna Kadelburg,Ben Woolley

Publisher: Cambridge University Press

ISBN: 1316644383

Category: Juvenile Nonfiction

Page: 208

View: 912

New 2017 Cambridge A Level Maths and Further Maths resources to help students with learning and revision. Written for the OCR AS/A Level Further Mathematics specification for first teaching from 2017, this print Student Book covers the Pure Core content for AS and the first year of A Level. It balances accessible exposition with a wealth of worked examples, exercises and opportunities to test and consolidate learning, providing a clear and structured pathway for progressing through the course. It is underpinned by a strong pedagogical approach, with an emphasis on skills development and the synoptic nature of the course. Includes answers to aid independent study.

Writing Proofs in Analysis

Author: Jonathan M. Kane

Publisher: Springer

ISBN: 3319309676

Category: Mathematics

Page: 347

View: 5339

This is a textbook on proof writing in the area of analysis, balancing a survey of the core concepts of mathematical proof with a tight, rigorous examination of the specific tools needed for an understanding of analysis. Instead of the standard "transition" approach to teaching proofs, wherein students are taught fundamentals of logic, given some common proof strategies such as mathematical induction, and presented with a series of well-written proofs to mimic, this textbook teaches what a student needs to be thinking about when trying to construct a proof. Covering the fundamentals of analysis sufficient for a typical beginning Real Analysis course, it never loses sight of the fact that its primary focus is about proof writing skills. This book aims to give the student precise training in the writing of proofs by explaining exactly what elements make up a correct proof, how one goes about constructing an acceptable proof, and, by learning to recognize a correct proof, how to avoid writing incorrect proofs. To this end, all proofs presented in this text are preceded by detailed explanations describing the thought process one goes through when constructing the proof. Over 150 example proofs, templates, and axioms are presented alongside full-color diagrams to elucidate the topics at hand.

The Elements of Advanced Mathematics, Fourth Edition

Author: Steven G. Krantz

Publisher: CRC Press

ISBN: 1351378309

Category: Mathematics

Page: 390

View: 6220

This best-selling text has guided mathematics students through three editions. Fourth Edition streamlines the approach, aligning directly with the most common syllabi for this course. Number theory coverage is expanded. An introduction to cryptography shows students how mathematics is used in the real world and gives them the impetus for further exploration. This edition also includes more exercises sets in each chapter, expanded treatment of proofs, and new proof techniques. Continuing to bridge computationally oriented mathematics with more theoretically based mathematics, this text provides a path for students to understand higher level mathematic

Mathematical Finance

Core Theory, Problems and Statistical Algorithms

Author: Nikolai Dokuchaev

Publisher: Routledge

ISBN: 1134121989

Category: Business & Economics

Page: 208

View: 1344

Written in a rigorous yet logical and easy to use style, spanning a range of disciplines, including business, mathematics, finance and economics, this comprehensive textbook offers a systematic, self-sufficient yet concise presentation of the main topics and related parts of stochastic analysis and statistical finance that are covered in the majority of university programmes. Providing all explanations of basic concepts and results with proofs and numerous examples and problems, it includes: an introduction to probability theory a detailed study of discrete and continuous time market models a comprehensive review of Ito calculus and statistical methods as a basis for statistical estimation of models for pricing a detailed discussion of options and their pricing, including American options in a continuous time setting. An excellent introduction to the topic, this textbook is an essential resource for all students on undergraduate and postgraduate courses and advanced degree programs in econometrics, finance, applied mathematics and mathematical modelling as well as academics and practitioners.

Proofs and Fundamentals

A First Course in Abstract Mathematics

Author: Ethan D. Bloch

Publisher: Springer Science & Business Media

ISBN: 1461221307

Category: Mathematics

Page: 424

View: 1327

The aim of this book is to help students write mathematics better. Throughout it are large exercise sets well-integrated with the text and varying appropriately from easy to hard. Basic issues are treated, and attention is given to small issues like not placing a mathematical symbol directly after a punctuation mark. And it provides many examples of what students should think and what they should write and how these two are often not the same.

Discrete Mathematics

Proof Techniques and Mathematical Structures

Author: R. C. Penner

Publisher: World Scientific

ISBN: 9789810240882

Category: Computers

Page: 469

View: 9051

This book offers an introduction to mathematical proofs and to the fundamentals of modern mathematics. No real prerequisites are needed other than a suitable level of mathematical maturity. The text is divided into two parts, the first of which constitutes the core of a one-semester course covering proofs, predicate calculus, set theory, elementary number theory, relations, and functions, and the second of which applies this material to a more advanced study of selected topics in pure mathematics, applied mathematics, and computer science, specifically cardinality, combinatorics, finite-state automata, and graphs. In both parts, deeper and more interesting material is treated in optional sections, and the text has been kept flexible by allowing many different possible courses or emphases based upon different paths through the volume.


The Core Course for A-level

Author: Linda Bostock,Suzanne Chandler

Publisher: Nelson Thornes

ISBN: 9780859503068

Category: Juvenile Nonfiction

Page: 752

View: 4687

Written for the Edexcel Syllabus B and similar schemes offered by the major Awarding Bodies. The authors have incorported many modern approaches to mathematical understanding whilst retaining the most effective traditional methods. Plenty of worked examples and stimulating exercises also support this highly popular text.

How to Think about Analysis

Author: Lara Alcock

Publisher: Oxford University Press, USA

ISBN: 0198723539

Category: Mathematics

Page: 246

View: 9858

Analysis is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared.

Advanced Problems in Mathematics

Preparing for University

Author: Stephen Siklos

Publisher: Open Book Publishers

ISBN: 1783741449

Category: Mathematics

Page: 186

View: 7655

This book is intended to help students prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Papers). STEP examinations are used by Cambridge colleges as the basis for conditional offers in mathematics and sometimes in other mathematics-related subjects. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on past papers to become accustomed to university-style mathematics. Advanced Problems in Mathematics is recommended as preparation for any undergraduate mathematics course, even for students who do not plan to take the Sixth Term Examination Paper. The questions analysed in this book are all based on recent STEP questions selected to address the syllabus for Papers I and II, which is the A-level core (i.e. C1 to C4) with a few additions. Each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anybody interested in advanced mathematics.

A Transition to Mathematics with Proofs

Author: Michael J Cullinane

Publisher: Jones & Bartlett Publishers

ISBN: 1449627781

Category: Mathematics

Page: 354

View: 9825

Developed for the "transition" course for mathematics majors moving beyond the primarily procedural methods of their calculus courses toward a more abstract and conceptual environment found in more advanced courses, A Transition to Mathematics with Proofs emphasizes mathematical rigor and helps students learn how to develop and write mathematical proofs. The author takes great care to develop a text that is accessible and readable for students at all levels. It addresses standard topics such as set theory, number system, logic, relations, functions, and induction in at a pace appropriate for a wide range of readers. Throughout early chapters students gradually become aware of the need for rigor, proof, and precision, and mathematical ideas are motivated through examples.

Exploring Mathematics

An Engaging Introduction to Proof

Author: John Meier,Derek Smith

Publisher: Cambridge University Press

ISBN: 1107128986

Category: Mathematics

Page: 300

View: 6398

Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with selected additional topics that provide many possibilities for further exploration. With a problem-based approach to investigating the material, students develop interesting examples and theorems through numerous exercises and projects. In-text exercises, with complete solutions or robust hints included in an appendix, help students explore and master the topics being presented. The end-of-chapter exercises and projects provide students with opportunities to confirm their understanding of core material, learn new concepts, and develop mathematical creativity.

The Art of Proof

Basic Training for Deeper Mathematics

Author: Matthias Beck,Ross Geoghegan

Publisher: Springer Science & Business Media

ISBN: 9781441970237

Category: Mathematics

Page: 182

View: 1696

The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.

Discrete Mathematics

Proofs, Structures and Applications, Third Edition

Author: Rowan Garnier,John Taylor

Publisher: CRC Press

ISBN: 1439812802

Category: Mathematics

Page: 843

View: 6881

Taking an approach to the subject that is suitable for a broad readership, Discrete Mathematics: Proofs, Structures, and Applications, Third Edition provides a rigorous yet accessible exposition of discrete mathematics, including the core mathematical foundation of computer science. The approach is comprehensive yet maintains an easy-to-follow progression from the basic mathematical ideas to the more sophisticated concepts examined later in the book. This edition preserves the philosophy of its predecessors while updating and revising some of the content. New to the Third Edition In the expanded first chapter, the text includes a new section on the formal proof of the validity of arguments in propositional logic before moving on to predicate logic. This edition also contains a new chapter on elementary number theory and congruences. This chapter explores groups that arise in modular arithmetic and RSA encryption, a widely used public key encryption scheme that enables practical and secure means of encrypting data. This third edition also offers a detailed solutions manual for qualifying instructors. Exploring the relationship between mathematics and computer science, this text continues to provide a secure grounding in the theory of discrete mathematics and to augment the theoretical foundation with salient applications. It is designed to help readers develop the rigorous logical thinking required to adapt to the demands of the ever-evolving discipline of computer science.

Handbook of Proof Theory

Author: S.R. Buss

Publisher: Elsevier

ISBN: 9780080533186

Category: Mathematics

Page: 810

View: 8657

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

Mathematical Analysis and Proof

Author: David S. G. Stirling

Publisher: Horwood Publishing, Limited

ISBN: 9781898563365

Category: Mathematics

Page: 243

View: 1216

This text addresses a weakness observed among students, namely a lack of familiarity with formal proof. Dr. Stirling begins with the idea of mathematical proof and the need for it, devoting care to develop associated technical and logical skills. This is then brought to bear on the core material of analysis and a presentation that the development reads naturally and in straight-forward progression, not only by giving proofs, but also indicating how they are constructed. This approach offers intellectual challenge and stimulus to readers by emphasizing two important points: the need for familiarity with long mathematical arguments and manipulation; and the importance of the ability to construct proofs in analysis.

Curvature in Mathematics and Physics

Author: Shlomo Sternberg

Publisher: Courier Corporation

ISBN: 0486292711

Category: Mathematics

Page: 416

View: 9614

Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.

The Mathematics of Signal Processing

Author: Steven B. Damelin,Willard Miller, Jr

Publisher: Cambridge University Press

ISBN: 1107013224

Category: Mathematics

Page: 449

View: 9670

Arising from courses taught by the authors, this largely self-contained treatment is ideal for mathematicians who are interested in applications or for students from applied fields who want to understand the mathematics behind their subject. Early chapters cover Fourier analysis, functional analysis, probability and linear algebra, all of which have been chosen to prepare the reader for the applications to come. The book includes rigorous proofs of core results in compressive sensing and wavelet convergence. Fundamental is the treatment of the linear system y=Φx in both finite and infinite dimensions. There are three possibilities: the system is determined, overdetermined or underdetermined, each with different aspects. The authors assume only basic familiarity with advanced calculus, linear algebra and matrix theory and modest familiarity with signal processing, so the book is accessible to students from the advanced undergraduate level. Many exercises are also included.

Find eBook