Download or read book A Gateway to Higher Mathematics written by Jason H. Goodfriend and published by Jones & Bartlett Learning. This book was released on 2005 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Gateway to Abstract Mathematics written by and published by CUP Archive. This book was released on with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Algebra Gateway to Mathematics Second Edition written by Robert Messer and published by American Mathematical Soc.. This book was released on 2021-07-12 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Algebra: Gateway to Mathematics uses linear algebra as a vehicle to introduce students to the inner workings of mathematics. The structures and techniques of mathematics in turn provide an accessible framework to illustrate the powerful and beautiful results about vector spaces and linear transformations. The unifying concepts of linear algebra reveal the analogies among three primary examples: Euclidean spaces, function spaces, and collections of matrices. Students are gently introduced to abstractions of higher mathematics through discussions of the logical structure of proofs, the need to translate terminology into notation, and efficient ways to discover and present proofs. Application of linear algebra and concrete examples tie the abstract concepts to familiar objects from algebra, geometry, calculus, and everyday life. Students will finish a course using this text with an understanding of the basic results of linear algebra and an appreciation of the beauty and utility of mathematics. They will also be fortified with a degree of mathematical maturity required for subsequent courses in abstract algebra, real analysis, and elementary topology. Students who have prior background in dealing with the mechanical operations of vectors and matrices will benefit from seeing this material placed in a more general context.
Download or read book An Invitation to Abstract Mathematics written by Béla Bajnok and published by Springer Nature. This book was released on 2020-10-27 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook promotes an active transition to higher mathematics. Problem solving is the heart and soul of this book: each problem is carefully chosen to demonstrate, elucidate, or extend a concept. More than 300 exercises engage the reader in extensive arguments and creative approaches, while exploring connections between fundamental mathematical topics. Divided into four parts, this book begins with a playful exploration of the building blocks of mathematics, such as definitions, axioms, and proofs. A study of the fundamental concepts of logic, sets, and functions follows, before focus turns to methods of proof. Having covered the core of a transition course, the author goes on to present a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices touch on historical perspectives, current trends, and open questions, showing mathematics as a vibrant and dynamic human enterprise. This second edition has been reorganized to better reflect the layout and curriculum of standard transition courses. It also features recent developments and improved appendices. An Invitation to Abstract Mathematics is ideal for those seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics, as well as non-math majors interested in exploring higher-level concepts. From reviews of the first edition: Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. ... The book can be used as a text for traditional transition or structure courses ... but since Bajnok invites all students, not just mathematics majors, to enjoy the subject, he assumes very little background knowledge. Jill Dietz, MAA Reviews The style of writing is careful, but joyously enthusiastic.... The author’s clear attitude is that mathematics consists of problem solving, and that writing a proof falls into this category. Students of mathematics are, therefore, engaged in problem solving, and should be given problems to solve, rather than problems to imitate. The author attributes this approach to his Hungarian background ... and encourages students to embrace the challenge in the same way an athlete engages in vigorous practice. John Perry, zbMATH
Download or read book A Gateway to Abstract Mathematics written by Edwin Arthur Maxwell and published by . This book was released on 1965 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Download or read book Abstract Algebra written by John W. Lawrence and published by Cambridge University Press. This book was released on 2021-04-15 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through this book, upper undergraduate mathematics majors will master a challenging yet rewarding subject, and approach advanced studies in algebra, number theory and geometry with confidence. Groups, rings and fields are covered in depth with a strong emphasis on irreducible polynomials, a fresh approach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory and its applications to polynomial equations and geometric constructions are treated in depth. Those interested in computations will appreciate the novel treatment of division algorithms. This rigorous text 'gets to the point', focusing on concisely demonstrating the concept at hand, taking a 'definitions first, examples next' approach. Exercises reinforce the main ideas of the text and encourage students' creativity.
Download or read book An Introduction to Abstract Algebra written by F. M. Hall and published by CUP Archive. This book was released on 1966 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A summary of basic group theory is followed by accounts of group homomorphisms, rings, fields and integral domains. The book is intended both for those who wish to know something about modern algebra and also for those already familiar with the elements of the subject who wish to study further.
Download or read book An Introduction to Proofs with Set Theory written by Daniel Ashlock and published by Morgan & Claypool Publishers. This book was released on 2020-06-24 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid's algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor's Paradox, Russel's Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of Gödel's Incompleteness Theorems.
Download or read book Introduction to Contextual Maths in Chemistry written by Fiona Dickinson and published by Royal Society of Chemistry. This book was released on 2023-01-17 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: CHEMISTRY STUDENT GUIDES. GUIDED BY STUDENTS For any student who has ever struggled with a mathematical understanding of chemistry, this book is for you. Mathematics is the essential tool for physical scientists. We know that confidence in using mathematics early on in a chemistry degree builds a solid foundation for further study. However, applying the abstract mathematics taught in schools to chemical phenomena is one of the biggest challenges that chemistry students face. In this book, we take a ‘chemistry-first’ approach. We link the mathematics to recognisable chemical concepts, building on high school chemistry, to facilitate deeper understanding. We cover the practical mathematical skills, including representation of data as tables and graphs, and give an overview of error handling in the physical sciences. More advanced mathematical concepts are introduced, using calculus to determine kinetic rate laws, intermolecular forces and in quantifying energetic change in thermodynamics. We also introduce the concept of the complex number and its role in considering quantum wave functions, widely used in computational chemistry. There are worked examples and problem sets to provide plenty of practise material to build proficiency. We also include insights from real students, which identify common problem areas and provide the prompts that helped them to overcome these. Chemistry Student Guides are written with current students involved at every stage, guiding the books towards the most challenging aspects of the topic.
Download or read book Abstract Algebra with Applications written by Audrey Terras and published by Cambridge University Press. This book was released on 2019 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers a friendly and concise introduction to abstract algebra, emphasizing its uses in the modern world.
Download or read book Connecting Abstract Algebra to Secondary Mathematics for Secondary Mathematics Teachers written by Nicholas H. Wasserman and published by Springer. This book was released on 2018-12-12 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Secondary mathematics teachers are frequently required to take a large number of mathematics courses – including advanced mathematics courses such as abstract algebra – as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely connected. Yet, despite this connection many secondary teachers insist that such advanced mathematics is unrelated to their future professional work in the classroom. This edited volume elaborates on some of the connections between abstract algebra and secondary mathematics, including why and in what ways they may be important for secondary teachers. Notably, the volume disseminates research findings about how secondary teachers engage with, and make sense of, abstract algebra ideas, both in general and in relation to their own teaching, as well as offers itself as a place to share practical ideas and resources for secondary mathematics teacher preparation and professional development. Contributors to the book are scholars who have both experience in the mathematical preparation of secondary teachers, especially in relation to abstract algebra, as well as those who have engaged in related educational research. The volume addresses some of the persistent issues in secondary mathematics teacher education in connection to advanced mathematics courses, as well as situates and conceptualizes different ways in which abstract algebra might be influential for teachers of algebra. Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers is a productive resource for mathematics teacher educators who teach capstone courses or content-focused methods courses, as well as for abstract algebra instructors interested in making connections to secondary mathematics.
Download or read book Gateway to Memory written by Mark A. Gluck and published by MIT Press. This book was released on 2001 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for students and researchers who have a specific interest in learning and memory and want to understand how computational models can be integrated into experimental research on the hippocampus and learning. It emphasizes the function of brain structures as they give rise to behavior, rather than the molecular or neuronal details. It also emphasizes the process of modeling, rather than the mathematical details of the models themselves. The book is divided into two parts. The first part provides a tutorial introduction to topics in neuroscience, the psychology of learning and memory, and the theory of neural network models. The second part, the core of the book, reviews computational models of how the hippocampus cooperates with other brain structures -- including the entorhinal cortex, basal forebrain, cerebellum, and primary sensory and motor cortices -- to support learning and memory in both animals and humans. The book assumes no prior knowledge of computational modeling or mathematics. For those who wish to delve more deeply into the formal details of the models, there are optional "mathboxes" and appendices. The book also includes extensive references and suggestions for further readings.
Download or read book Bridge to Abstract Mathematics written by Ronald P. Morash and published by . This book was released on 1991 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is designed for students who are preparing to take a post-calculus abstract algebra and analysis course. Morash concentrates on providing students with the basic tools (sets, logic and proof techniques) needed for advanced study in mathematics. The first six chapters of the text are devoted to these basics, and these topics are reinforced throughout the remainder of the text. Morash guides students through the transition from a calculus-level courses upper-level courses that have significant abstract mathematical content.
Download or read book The Education of T C MITS written by Lillian R. Lieber and published by Paul Dry Books. This book was released on 2007-06-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whether you are stumped by the "commutative law" in algebra or a whiz at multiplying three-digit numbers in your head, this book opens the door to the wonders of mathematical imagining. By using simple language and intriguing illustrations drawn by her husband, Hugh, Lillian Lieber presents subtle mathematical concepts in an easy-to-understand way. Over sixty years after its release, this whimsical exploration of how to think in a mathematical mood will continue to delight math-lovers of all ages. Barry Mazur's new introduction is a tribute to the Liebers' influence on generations of mathematicians.
Download or read book Mathematics Galore written by James Tanton and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Galore! Showcases some of the best activities and student outcomes of the St. Mark's Institute of Mathematics and invites you to engage the mathematics yourself! Revel in the delight of deep intellectual play and marvel at the heights to which young scholars can rise. See some great mathematics explained and proved via natural and accessible means. Based on 26 essays ( newsletters ) and eight additional pieces, Mathematics Galore! offers a large sample of mathematical tidbits and treasures, each immediately enticing, and each a gateway to layers of surprising depth and conundrum. Pick and read essays in no particular order and enjoy the mathematical stories that unfold. Be inspired for your courses, your math clubs and your math circles, or simply enjoy for yourself the bounty of research questions and intriguing puzzlers that lie within.
Download or read book Pure Math Discovering the Beauty of Abstract Mathematics written by Lexa N. Palmer and published by Book Lovers HQ. This book was released on 2024-09-30 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pure Math: Discovering the Beauty of Abstract Mathematics offers a unique approach to exploring the captivating world of pure mathematics. It's where logic meets imagination, and abstract thought gives rise to profound beauty. This book takes you beyond the formulas and calculations, uncovering the hidden elegance that lies at the heart of mathematical structures, patterns, and theories. From the concept of infinity to symmetry in group theory, this book delves into the core ideas of pure math that have fascinated thinkers for centuries. You’ll discover the aesthetic appeal of mathematical proofs, each one a treasure waiting to be unearthed, explore the intricate relationships in number theory, and journey through the strange worlds of non-Euclidean geometry and topology. Whether you're intrigued by the mysteries of prime numbers or the paradoxes that challenge conventional logic, Pure Math illuminates these abstract concepts in a way that is both engaging and intellectually stimulating. Written for those who appreciate the beauty of ideas, this book is a celebration of the intellectual creativity that drives pure mathematics. It's perfect for mathematicians, students, and curious readers who want to see math as more than a tool for problem-solving. It’s a testament to the wonder that can be found in abstract reasoning. What you will find in this book: The concept of infinity and its role in set theory and calculus The elegance of mathematical proofs and the joy of discovering them Patterns and symmetry in number theory, geometry, and algebra Paradoxes that challenge the boundaries of logic and intuition The philosophical implications of pure mathematics as a universal language Exploration of the beauty and complexity found in abstract mathematical structures Embark on a fascinating journey into the depths of pure mathematics and discover a new way of thinking about the world around you!
