Suggested Books Today | Books - Helge Scherlund's eLearning News

Check out these books below by Cambridge University Press.

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New Spaces in Mathematics - Formal and Conceptual Reflections

New Spaces in Mathematics
Formal and Conceptual Reflections

Mathematicians have long known that geometry is not absolute. Our understanding of what constitutes a 'space' has driven, and been driven by, significant applications inside and outside of mathematics...

This volume covers a broad range of topics in mathematics, including diffeologies, synthetic differential geometry, microlocal analysis, topos theory, infinity-groupoids, homotopy type theory, category-theoretic methods in geometry, stacks, derived geometry, and noncommutative geometry.

• Introduces a vast array of notions of 'space' in mathematics and physics, suitable for graduates and researchers
• Includes a mixture of formal introductions and more conceptual reflections, historical perspectives, and current open problems
• Contains chapters written by leading mathematicians and theoretical physicists (including two Fields Medallists)

Publication planned for: January 2021
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Combinatorial Mathematics

Combinatorial Mathematics

This long-awaited textbook is the most comprehensive introduction to a broad swath of combinatorial and discrete mathematics. The text covers enumeration, graphs, sets, and methods, and it includes both classical results and more recent developments. Assuming no prior exposure to combinatorics, it explains the basic material for graduate-level students in mathematics and computer science... 

Consistent notation and terminology are used throughout, allowing for a discussion of diverse topics in a unified language. The thorough bibliography, containing thousands of citations, makes this a valuable source for students and researchers alike.

• Can be used as a text for a one-year sequence, or as a one-semester introduction leading to an advanced course, with a complete solutions manual available online for instructors
• Contains more than 2200 exercises at various levels. Especially instructive, interesting, or valuable exercises are marked with a diamond symbol
• Includes several thousand references (with pointers to pages where cited) and many exercises, theorems, and proofs that have not previously appeared in textbooks

Date Published: July 2020
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Boolean Functions for Cryptography and Coding Theory 

Boolean Functions for Cryptography and Coding Theory

Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results...

The result is a complete and accessible text on the state of the art in single and multiple output Boolean functions that illustrates the interaction between mathematics, computer science, and telecommunications.

• A self-contained approach includes proofs for all the main results
• A detailed reference list points the reader to other key results and developments in the field
• Includes topics that have never been presented in monographs on Boolean functions, such as AMD codes, Gowers norm, and homomorphic encryption

Publication planned for: August 2020
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Beyond the Worst-Case Analysis of Algorithms

Beyond the Worst-Case Analysis of Algorithms

There are no silver bullets in algorithm design, and no single algorithmic idea is powerful and flexible enough to solve every computational problem. Nor are there silver bullets in algorithm analysis, as the most enlightening method for analyzing an algorithm often depends on the problem and the application...

Forty leading researchers have contributed introductions to different facets of this field, emphasizing the most important models and results, many of which can be taught in lectures to beginning graduate students in theoretical computer science and machine learning.

• Most chapters include open research directions and exercises suitable for classroom use
• First time this exciting research area has been covered by a book
• Many applications, especially in machine learning

Publication planned for: October 2020
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Source: Cambridge University Press.