Best Topology Books
Here you will get Best Topology Books For you.This is an up-to-date list of recommended books.
1. Curves for the Mathematically Curious: An Anthology of the Unpredictable, Historical, Beautiful, and Romantic
Author: by Julian Havil
Published at: Princeton University Press (October 15, 2019)
This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal.
Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral.
The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with.
3. Introduction to Topology: Third Edition (Dover Books on Mathematics)
Author: by Bert Mendelson
Published at: Dover Publications; Third edition (July 1, 1990)
Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems.
The book’s principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure. The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness.
In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space.
4. Lost in Math: How Beauty Leads Physics Astray
Author: by Sabine Hossenfelder
Published at: Basic Books; Illustrated edition (June 2, 2020)
In this “provocative” book (New York Times), a contrarian physicist argues that her field’s modern obsession with beauty has given us wonderful math but bad science. Whether pondering black holes or predicting discoveries at CERN, physicists believe the best theories are beautiful, natural, and elegant, and this standard separates popular theories from disposable ones.
This is why, Sabine Hossenfelder argues, we have not seen a major breakthrough in the foundations of physics for more than four decades. The belief in beauty has become so dogmatic that it now conflicts with scientific objectivity: observation has been unable to confirm mindboggling theories, like supersymmetry or grand unification, invented by physicists based on aesthetic criteria.
Worse, these “too good to not be true” theories are actually untestable and they have left the field in a cul-de-sac. To escape, physicists must rethink their methods. Only by embracing reality as it is can science discover the truth.
5. Algebraic Topology
Author: by Allen Hatcher
Published at: Cambridge University Press; 1st edition (December 1, 2001)
In most major universities one of the three or four basic first year graduate mathematics courses is algebraic topology. This introductory text is suitable for use in a course on the subject or for self study, featuring broad coverage and a readable exposition, with many examples and exercises.
The four main chapters present the basics: fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory generally. The author emphasizes the geometric aspects of the subject, which helps students gain intuition. A unique feature is the inclusion of many optional topics not usually part of a first course due to time constraints: Bockstein and transfer homomorphisms, direct and inverse limits, H spaces and Hopf algebras, the Brown representability theorem, the James reduced product, the Dold Thom theorem, and Steenrod squares and powers.
6. Speedsolving the Cube: Easy-to-Follow, Step-by-Step Instructions for Many Popular 3-D Puzzles
Author: by Dan Harris
Sterling; Illustrated edition (May 1, 2008)
Super Strategies for Speedcubers! For many of us, simply being able to solve Rubik’s Cube is not rewarding enough. Solving it as fast as possible is the exciting part! They call it speedcubinga mind-bending blur of quick twists and turns that solves Rubik’s Cube in times that have been clocked at less than 20 seconds.
Today, thanks to the 2003 revival of the Rubik’s World Championships, speedcubing is spreading like wildfire. Here, complete with detailed illustrations and basic as well as advanced solving techniques, is the ultimate speedcuber’s guide. It not only gives the solution to the familiar 3x3x3 cube (which has 43,252,003,274,489,856,000that’s 43 quintillionpossible positions), but also the 2x2x2, 4x4x4, and staggeringly difficult 5x5x5 puzzles.
With millions of cubes out there and countless would-be champions looking for tips to improve their times, this is the definitive manual for this unique sport.
7. Topology (Classic Version) (Pearson Modern Classics for Advanced Mathematics Series)
Author: by James Munkres
Published at: Pearson; 2nd edition (March 10, 2017)
For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately. This title is part of the Pearson Modern Classics series.
Pearson Modern Classics are acclaimed titles at a value price.Please visit www.Pearsonhighered. Com/math-classics-series for a complete list of titles. This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses.
Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences.
8. A Visual Introduction to Differential Forms and Calculus on Manifolds
Author: by Jon Pierre Fortney
Published at: Springer; 1st ed. 2018 edition (November 15, 2018)
This book explains and helps readers to develop geometric intuition as it relates to differential forms. It includes over 250 figures to aid understanding and enable readers to visualize the concepts being discussed. The author gradually builds up to the basic ideas and concepts so that definitions, when made, do not appear out of nowhere, and both the importance and role that theorems play is evident as or before they are presented.
With a clear writing style and easy-to- understand motivations for each topic, this book is primarily aimed at second- or third-year undergraduate math and physics students with a basic knowledge of vector calculus and linear algebra.
9. An Introduction to Manifolds (Universitext)
Author: by Loring W. Tu
Published at: Springer; 2nd ed. 2011 edition (October 6, 2010)
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics.
By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way, the reader acquires the knowledge and skills necessary for further study of geometry and topology.
The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study.
10. GRE Prep 2021 2022: The most complete and up-to-date GRE study book! 4 Full-Length practice tests + review & techniques for the Graduate Record Examination
Author: by Innotion Academic Prep
Published at: Independently published (January 17, 2021)
Do you want to love your GRE score? Are you looking to ACE the exam and get into the Graduate School of your dreams? Do you want to walk into the test center feeling confident and calm? Then keep reading, because the new Innotion GRE Prep 2021-2022 is what you need!
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Create optimal study habits prior to and on the final day before any exam. Walk into the exam room knowing you’ll get the exact score you desire. Designed specifically to ensure you learn faster, retain more, and ACE the GRE, the all-new GRE Exam Prep is based on the ETS GRE Information and provides everything you need to thoroughly prepare for and crush the exam.
11. Introducing MATH! Grade 4 by ArgoPrep: 600+ Practice Questions + Comprehensive Overview of Each Topic + Detailed Video Explanations Included | 4th … (Introducing MATH! Series by ArgoPrep)
Author: by Argo Brothers
Published at: Argo Brothers (May 1, 2019)
Introducing Math!By ArgoPrep is an award-winning series created by certified teachers to provide students with high-quality practice problems. This workbook is designed to provide you with a comprehensive overview of Grade 4 mathematics. Our workbooks include topic overviews with instruction, practice questions, answer explanations along with free digital access to video explanations.
Practice in confidence – with ArgoPrep! Grade 4 Mathematics:Chapter 1 – Operations and Algebraic Thinking1.1. Use the four operations with whole numbers to solve problems.1.2. Gain familiarity with factors and multiples.1.3. Generate and analyze patterns. Chapter 2 – Numbers & Operation in Base Ten2.1.
Generalize place value understanding for multi-digit whole numbers.2.2. Use place value understanding and properties of operations to perform multi-digit arithmetic. Chapter 3 – Fractions3.1. Extend understanding of fraction equivalence and ordering.3.2. Build fraction from unit fractions3.3. Understand decimal notation for fractions, and compare decimal fractionsChapter 4 – Measurement and Data 4.1.
12. IAAT2 Practice Tests (Mr. Rhee's Brilliant Math)
Author: by Yeon Rhee
Published at: CreateSpace Independent Publishing Platform; 1st edition (December 31, 2016)
This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles, and Chern forms that are helpful for a deeper understanding of both classical and modern physics and engineering.
It is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. A main addition introduced in this Third Edition is the inclusion of an Overview, which can be read before starting the text.
This appears at the beginning of the text, before Chapter 1. Many of the geometric concepts developed in the text are previewed here and these are illustrated by their applications to a single extended problem in engineering, namely the study of the Cauchy stresses created by a small twist of an elastic cylindrical rod about its axis.
14. The Wheel Of Time: The Shamans Of Mexico Their Thoughts About Life Death And The Universe
Author: by Carlos Castaneda
Published at: Washington Square Press; Later Printing (8th) edition (January 1, 2001)
World-renowned bestselling author Carlos Castaneda’s Selection of his wrtings on the shamans of ancient Mexico. Originally drawn to Yaqui Indian spiritual leader don Juan Matus for his knowledge of mind-altering plants, bestselling author Carlos Castaneda soon immersed himself in the sorcerer’s magical world entirely.
Ten years after his first encounter with the shaman, Castaneda examines his field notes and comes to understand what don Juan knew all alongthat these plants are merely a means to understanding the alternative realities that one cannot fully embrace on one’s own.
In Journey to Ixtlan, Carlos Castaneda introduces readers to this new approach for the first time and explores, as he comes to experience it himself, his own final voyage into the teachings of don Juan, sharing with us what it is like to truly stop the world and perceive reality on his own terms.
15. Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life
Author: by Albert-László Barabási
Published at: Basic Books; Illustrated edition (June 24, 2014)
The best-selling guide to network science, the revolutionary field that reveals the deep links between all forms of human social life A cocktail party.A terrorist cell.Ancient bacteria. An international conglomerate. All are networks, and all are a part of a surprising scientific revolution.
In Linked, Albert-Llrab, the nation’s foremost expert in the new science of networks, takes us on an intellectual adventure to prove that social networks, corporations, and living organisms are more similar than previously thought. Barab shows that grasping a full understanding of network science will someday allow us to design blue-chip businesses, stop the outbreak of deadly diseases, and influence the exchange of ideas and information.
Just as James Gleick and the Erdos-Ri model brought the discovery of chaos theory to the general public, Linked tells the story of the true science of the future and of experiments in statistical mechanics on the internet, all vital parts of what would eventually be called the Barab-Albert model.