Complex Variables (Dover Books on Mathematics)

By Francis J. Flanigan

A warning to arithmetic professors: Complex Variables does no longer stick with traditional outlines in fact fabric. One reviewer noting its originality wrote: "A usual textual content is usually most well liked [to a superb textual content like this] as the professor understands the order of issues and the issues, and does not relatively need to concentrate on the textual content. He can visit classification with no preparation." no longer so right here — Dr. Flanigan treats this most vital box of latest arithmetic in a most unique method. whereas the entire fabric for a complicated undergraduate or first-year graduate direction is roofed, dialogue of complicated algebra is not on time for a hundred pages, until eventually harmonic services were analyzed from a true variable point of view. scholars who've forgotten or by no means handled this fabric will locate it precious for the following features. moreover, analytic capabilities are outlined in a manner which simplifies the following idea. Contents contain: Calculus within the aircraft, Harmonic features within the aircraft, complicated Numbers and complicated services, Integrals of Analytic features, Analytic capabilities and gear sequence, Singular issues and Laurent sequence, The Residue Theorem and the Argument precept, and Analytic capabilities as Conformal Mappings.
Those accustomed to arithmetic texts will observe the tremendous illustrations all through and massive variety of difficulties provided on the bankruptcy ends. a solution part is equipped. scholars weary of plodding mathematical prose will locate Professor Flanigan's sort as fresh and stimulating as his approach.

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Mod Two Homology and Cohomology (Universitext)

Cohomology and homology modulo 2 is helping the reader take hold of extra quite simply the fundamentals of an enormous instrument in algebraic topology. in comparison to a extra normal method of (co)homology this fresh strategy has many pedagogical advantages:

1. It leads extra speedy to the necessities of the subject,
2. a lack of symptoms and orientation concerns simplifies the theory,
3. Computations and complicated purposes will be provided at an previous level,
4. easy geometrical interpretations of (co)chains.

Mod 2 (co)homology was once built within the first area of the 20th century instead to critical homology, earlier than either turned specific situations of (co)homology with arbitrary coefficients.

The first chapters of this e-book may perhaps function a foundation for a graduate-level introductory path to (co)homology. Simplicial and singular mod 2 (co)homology are brought, with their items and Steenrod squares, in addition to equivariant cohomology. Classical functions comprise Brouwer's fastened element theorem, Poincaré duality, Borsuk-Ulam theorem, Hopf invariant, Smith thought, Kervaire invariant, and so on. The cohomology of flag manifolds is handled intimately (without spectral sequences), together with the connection among Stiefel-Whitney periods and Schubert calculus. more moderen advancements also are lined, together with topological complexity, face areas, equivariant Morse conception, conjugation areas, polygon areas, among others. each one bankruptcy ends with workouts, with a few tricks and solutions on the finish of the book.

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Geometric Methods and Applications : For Computer Science and Engineering

By Jean Gallier

This publication is an advent to the elemental options and instruments wanted for fixing difficulties of a geometrical nature utilizing a working laptop or computer. It makes an attempt to fill the space among normal geometry books, that are essentially theoretical, and utilized books on special effects, computing device imaginative and prescient, robotics, or desktop studying.

 This booklet covers the subsequent issues: affine geometry, projective geometry, Euclidean geometry, convex units, SVD and primary part research, manifolds and Lie teams, quadratic optimization, fundamentals of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). a few functional purposes of the strategies offered during this booklet contain desktop imaginative and prescient, extra in particular contour grouping, movement interpolation, and robotic kinematics.

  In this greatly up-to-date moment variation, extra fabric on convex units, Farkas’s lemma, quadratic optimization and the Schur supplement were additional. The bankruptcy on SVD has been enormously improved and now features a presentation of PCA.

 The publication is definitely illustrated and has bankruptcy summaries and loads of routines all through. will probably be of curiosity to a large viewers together with desktop scientists, mathematicians, and engineers.

 Reviews of first edition:

"Gallier's ebook should be an invaluable resource for a person drawn to functions of geometrical how to remedy difficulties that come up in a variety of branches of engineering. it may well aid to improve the subtle recommendations from the extra complicated components of geometry into precious instruments for applications." (Mathematical studies, 2001)

" might be worthy as a reference ebook for postgraduates wishing to discover the relationship among their present challenge and the underlying geometry." (The Australian Mathematical Society, 2001)

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An Introduction to Differential Equations and Their Applications (Dover Books on Mathematics)

By Stanley J. Farlow

Intended to be used in a starting one-semester direction in differential equations, this article is designed for college kids of natural and utilized arithmetic with a operating wisdom of algebra, trigonometry, and hassle-free calculus. Its mathematical rigor is balanced by way of whole yet basic causes that entice readers' actual and geometric intuition.
Starting with an advent to differential equations, the textual content proceeds to examinations of first- and second-order differential equations, sequence strategies, the Laplace rework, structures of differential equations, distinction equations, nonlinear differential equations and chaos, and partial differential equations. a variety of figures, issues of suggestions, and historic notes make clear the text.

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How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics

What is math? How precisely does it paintings? And what do 3 siblings attempting to proportion a cake need to do with it? In How to Bake Pi, math professor Eugenia Cheng offers an obtainable creation to the common sense and wonder of arithmetic, powered, suddenly, by means of insights from the kitchen. We learn the way the béchamel in a lasagna could be a lot just like the quantity 5, and why creating a strong custard proves that math is simple yet lifestyles is difficult. on the center of all of it is Cheng’s paintings on type thought, a state of the art “mathematics of mathematics,” that's approximately realizing how math works.

Combined together with her infectious enthusiasm for cooking and precise zest for all times, Cheng’s point of view on math is a humorous trip via an unlimited territory no renowned e-book on math has explored earlier than. So, what's math? Let’s search for the reply within the kitchen.

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Here's Looking at Euclid: A Surprising Excursion Through the Astonishing World of Math

By Alex Bellos

Too frequently math will get a foul rap, characterised as dry and hard. yet, Alex Bellos says, "math should be inspiring and brilliantly artistic. Mathematical proposal is likely one of the nice achievements of the human race, and arguably the root of all human growth. the realm of arithmetic is a extraordinary place."

Bellos has traveled everywhere in the globe and has plunged into background to discover attention-grabbing tales of mathematical success, from the breakthroughs of Euclid, the best mathematician of all time, to the creations of the Zen grasp of origami, one of many most popular components of mathematical paintings this day. Taking us into the wilds of the Amazon, he tells the tale of a tribe there who can count number simply to 5 and reviews at the most recent findings in regards to the math instinct—including the revelation that ants can truly count number what number steps they’ve taken. visiting to the Bay of Bengal, he interviews a Hindu sage in regards to the awesome mathematical insights of the Buddha, whereas in Japan he visits the godfather of Sudoku and introduces the brainteasing delights of mathematical games.

Exploring the mysteries of randomness, he explains why it really is most unlikely for our iPods to really randomly decide on songs. In probing the numerous intrigues of that almost all cherished of numbers, pi, he visits with brothers so captivated with the elusive quantity that they outfitted a supercomputer of their long island house to check it. all through, the adventure is better with a wealth of exciting illustrations, reminiscent of of the shrewdpermanent puzzles referred to as tangrams and the crochet production of an American math professor who without notice learned sooner or later that she may perhaps knit a illustration of upper dimensional area that not anyone have been capable of visualize.

Whether writing approximately how algebra solved Swedish site visitors difficulties, vacationing the psychological Calculation international Cup to reveal the secrets and techniques of lightning calculation, or exploring the hyperlinks among pineapples and lovely the teeth, Bellos is a superbly attractive consultant who by no means fails to thrill whilst he edifies. Here’s Euclid is an extraordinary gem that brings the wonderful thing about math to existence.

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Algebra Know-It-ALL: Beginner to Advanced, and Everything in Between

By Stan Gibilisco

Master algebra from the relaxation of home!

Want to “know all of it” by way of algebra? Algebra Know-It-ALL gives you the professional, one-on-one guide you would like, no matter if you are new to algebra or you are looking to ramp up your talents. supplying easy-to-understand strategies and punctiliously defined routines, math whiz Stan Gibilisco serves as your personal inner most tutor-without the cost! His transparent, pleasant advice is helping you take on the techniques and difficulties that confuse you the main and paintings via them at your individual velocity.

Train your mind conveniently! Algebra Know-It-ALL features:

  • Icons that will help you determine your present ability point
  • Chapter-end quizzes and observe problem/solution pairs to augment studying
  • Worked-out solutions to all perform routines
  • Extensive multiple-choice inquiries to organize you for standardized checks
  • “Extra credits” and “Challenge” difficulties to stretch your skills

Stan's specialist advice delivers the information to:

  • Solve mathematics difficulties with out a calculator
  • Convert fractions to decimal shape and vice-versa
  • Manipulate uncomplicated equations and inequalities
  • Learn how coordinate platforms paintings
  • Make easy graphs
  • Solve quadratic and cubic equations
  • Understand complex-number strategies to equations
  • Use logarithms and exponential features
  • Take collage front examinations with self belief li>And a lot more!

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Introduction to Abstract Algebra

By W. Keith Nicholson

Praise for the 3rd Edition

". . . an expository masterpiece of the top didactic worth that has won extra attractivity throughout the numerous advancements . . ."—Zentralblatt MATH

The Fourth variation of Introduction to summary Algebra maintains to supply an available method of the elemental buildings of summary algebra: teams, jewelry, and fields. The book's certain presentation is helping readers improve to summary concept via proposing concrete examples of induction, quantity idea, integers modulo n, and diversifications sooner than the summary buildings are outlined. Readers can instantly start to practice computations utilizing summary suggestions which are built in larger element later within the text.

The Fourth variation beneficial properties very important thoughts in addition to really expert issues, including:

  • The therapy of nilpotent teams, together with the Frattini and becoming subgroups

  • Symmetric polynomials

  • The evidence of the elemental theorem of algebra utilizing symmetric polynomials

  • The evidence of Wedderburn's theorem on finite department rings

  • The facts of the Wedderburn-Artin theorem

Throughout the booklet, labored examples and real-world difficulties illustrate thoughts and their purposes, facilitating an entire knowing for readers despite their history in arithmetic. A wealth of computational and theoretical workouts, starting from simple to complicated, permits readers to check their comprehension of the fabric. additionally, specified old notes and biographies of mathematicians supply context for and light up the dialogue of key themes. A options handbook can be to be had for readers who would favor entry to partial recommendations to the book's exercises.

Introduction to summary Algebra, Fourth Edition is a wonderful ebook for classes at the subject on the upper-undergraduate and beginning-graduate degrees. The publication additionally serves as a helpful reference and self-study instrument for practitioners within the fields of engineering, laptop technological know-how, and utilized mathematics.

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Geometry (Idiot's Guides)

By Sonal Bhatt, Rebecca Dayton

Almost about everybody takes a geometry category at one time or one other. And whereas a few humans fast snatch the techniques, such a lot locate geometry hard. masking every thing one might count on to come across in a highschool or collage path, Idiot's publications: Geometry covers every little thing a pupil would have to understand. This all-new booklet will combine workbook-like perform inquiries to strengthen the teachings. additionally, a word list of phrases, postulates, and theorems offer a brief connection with need-to-know details to boot. Easy-to-understand, step by step motives stroll the reader through:- fundamentals of Geometry- Reasoning and evidence- Perpendicular and Parallel traces- Congruent Triangles- homes of Triangles- Quadrilaterals- ameliorations- Similarity- correct Triangles and Trigonometry- Circles- sector of Polygons and Circles- floor zone and quantity

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Algebraic Combinatorics: Lectures at a Summer School in Nordfjordeid, Norway, June 2003 (Universitext)

By Peter Orlik

This e-book relies on sequence of lectures given at a summer season college on algebraic combinatorics on the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by means of Peter Orlik on hyperplane preparations, and the opposite one through Volkmar Welker on unfastened resolutions. either issues are crucial elements of present study in a number of mathematical fields, and the current ebook makes those subtle instruments to be had for graduate students.

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