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Math and Science Course Essentials

Math & Science Course Essentials

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'Astrobiology' cover image
Astrobiology

3rd Edition

Kevin W. Plaxco and Michael Gross

Informed by the discoveries and analyses of extrasolar planets and the findings from recent robotic missions across the solar system, scientists are rapidly replacing centuries of speculation about potential extraterrestrial habitats with real knowledge about the possibility of life outside our own biosphere—if it exists, and, if so, where. Casting new light on the biggest questions there are—how did we get here, and who else might be out there?—this third edition of Kevin W. Plaxco and Michael Gross's widely acclaimed Astrobiology incorporates a decade's worth of new developments in space to bring readers the most comprehensive, up-to-date, and engaging introduction to the field available.

Table of Contents

'Astrobiology' cover image
Astrobiology

3rd Edition

Kevin W. Plaxco and Michael Gross

Informed by the discoveries and analyses of extrasolar planets and the findings from recent robotic missions across the solar system, scientists are rapidly replacing centuries of speculation about potential extraterrestrial habitats with real knowledge about the possibility of life outside our own biosphere—if it exists, and, if so, where. Casting new light on the biggest questions there are—how did we get here, and who else might be out there?—this third edition of Kevin W. Plaxco and Michael Gross's widely acclaimed Astrobiology incorporates a decade's worth of new developments in space to bring readers the most comprehensive, up-to-date, and engaging introduction to the field available.

Table of Contents

'Astrobiology' cover image
Astrobiology

3rd Edition

Kevin W. Plaxco and Michael Gross

Informed by the discoveries and analyses of extrasolar planets and the findings from recent robotic missions across the solar system, scientists are rapidly replacing centuries of speculation about potential extraterrestrial habitats with real knowledge about the possibility of life outside our own biosphere—if it exists, and, if so, where. Casting new light on the biggest questions there are—how did we get here, and who else might be out there?—this third edition of Kevin W. Plaxco and Michael Gross's widely acclaimed Astrobiology incorporates a decade's worth of new developments in space to bring readers the most comprehensive, up-to-date, and engaging introduction to the field available.

Table of Contents

'Emmy Noether's Wonderful Theorem' cover image
Emmy Noether's Wonderful Theorem

Revised and Updated Edition

Dwight E. Neuenschwander

The year was 1915, and the young mathematician Emmy Noether had just settled into Göttingen University when Albert Einstein visited to lecture on his nearly finished general theory of relativity. Two leading mathematicians of the day, David Hilbert and Felix Klein, dug into the new theory with gusto, but had difficulty reconciling it with what was known about the conservation of energy. Knowing of her expertise in invariance theory, they requested Noether’s help. To solve the problem, she developed a novel theorem, applicable across all of physics, which relates conservation laws to continuous symmetries—one of the most important pieces of mathematical reasoning ever developed. In Dwight E. Neuenschwander’s new edition of Emmy Noether’s Wonderful Theorem, readers will encounter an updated explanation of Noether’s "first" theorem. The discussion of local gauge invariance has been expanded into a detailed presentation of the motivation, proof, and applications of the "second" theorem, including Noether’s resolution of concerns about general relativity.

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'Emmy Noether's Wonderful Theorem' cover image
Emmy Noether's Wonderful Theorem

Revised and Updated Edition

Dwight E. Neuenschwander

The year was 1915, and the young mathematician Emmy Noether had just settled into Göttingen University when Albert Einstein visited to lecture on his nearly finished general theory of relativity. Two leading mathematicians of the day, David Hilbert and Felix Klein, dug into the new theory with gusto, but had difficulty reconciling it with what was known about the conservation of energy. Knowing of her expertise in invariance theory, they requested Noether’s help. To solve the problem, she developed a novel theorem, applicable across all of physics, which relates conservation laws to continuous symmetries—one of the most important pieces of mathematical reasoning ever developed. In Dwight E. Neuenschwander’s new edition of Emmy Noether’s Wonderful Theorem, readers will encounter an updated explanation of Noether’s "first" theorem. The discussion of local gauge invariance has been expanded into a detailed presentation of the motivation, proof, and applications of the "second" theorem, including Noether’s resolution of concerns about general relativity.

Table of Contents

'Matrix Computations' cover image
Matrix Computations

4th Edition

Gene H. Golub and Charles F. Van Loan

The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool.

Table of Contents

'Matrix Computations' cover image
Matrix Computations

4th Edition

Gene H. Golub and Charles F. Van Loan

The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool.

Table of Contents

'Calculus in Context' cover image
Calculus in Context

Alexander J. Hahn

Breaking the mold of existing calculus textbooks, Calculus in Context draws students into the subject in two new ways. Part I develops the mathematical preliminaries (including geometry, trigonometry, algebra, and coordinate geometry) within the historical frame of the ancient Greeks and the heliocentric revolution in astronomy. Part II starts with comprehensive and modern treatments of the fundamentals of both differential and integral calculus, then turns to a wide-ranging discussion of applications. Students will learn that core ideas of calculus are central to concepts such as acceleration, force, momentum, torque, inertia, and the properties of lenses.

Table of Contents

'Calculus in Context' cover image
Calculus in Context

Alexander J. Hahn

Breaking the mold of existing calculus textbooks, Calculus in Context draws students into the subject in two new ways. Part I develops the mathematical preliminaries (including geometry, trigonometry, algebra, and coordinate geometry) within the historical frame of the ancient Greeks and the heliocentric revolution in astronomy. Part II starts with comprehensive and modern treatments of the fundamentals of both differential and integral calculus, then turns to a wide-ranging discussion of applications. Students will learn that core ideas of calculus are central to concepts such as acceleration, force, momentum, torque, inertia, and the properties of lenses.

Table of Contents

'Understanding Topology' cover image
Understanding Topology

Shaun V. Ault

The perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from mapping DNA to determining the shape of the universe, will engage students in a way traditional topology textbooks do not.

Table of Contents

'Understanding Topology' cover image
Understanding Topology

Shaun V. Ault

The perfect introductory topology textbook, Understanding Topology requires only a knowledge of calculus and a general familiarity with set theory and logic. Equally approachable and rigorous, the book's clear organization, worked examples, and concise writing style support a thorough understanding of basic topological principles. Professor Shaun V. Ault's unique emphasis on fascinating applications, from mapping DNA to determining the shape of the universe, will engage students in a way traditional topology textbooks do not.

Table of Contents

'From Music to Mathematics' cover image
From Music to Mathematics

Gareth E. Roberts

Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic.

Table of Contents

'From Music to Mathematics' cover image
From Music to Mathematics

Gareth E. Roberts

Taking a "music first" approach, Gareth E. Roberts's From Music to Mathematics will inspire students to learn important, interesting, and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich, the musical concepts and examples in the book motivate a deeper study of mathematics. Comprehensive and clearly written, From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation, scales, intervals, the circle of fifths, tonality, etc.), with the pertinent mathematics developed alongside the related musical topic.

Table of Contents

'Mathematics in Twentieth-Century Literature and Art' cover image
Mathematics in Twentieth-Century Literature and Art

Robert Tubbs

During the twentieth century, many artists and writers turned to abstract mathematical ideas to help them realize their aesthetic ambitions. Man Ray, Marcel Duchamp, and, perhaps most famously, Piet Mondrian used principles of mathematics in their work. Was it mere coincidence, or were these artists simply following their instincts, which in turn were ruled by mathematical underpinnings, such as optimal solutions for filling a space? If math exists within visual art, can it be found within literary pursuits? In short, just what is the relationship between mathematics and the creative arts? In this provocative, original exploration of mathematical ideas in art and literature, Robert Tubbs argues that the links are much stronger than previously imagined and exceed both coincidence and commonality of purpose. In the end, Tubbs makes the case that art can be better appreciated when the math that inspired it is better understood.

Table of Contents

'Mathematics in Twentieth-Century Literature and Art' cover image
Mathematics in Twentieth-Century Literature and Art

Robert Tubbs

During the twentieth century, many artists and writers turned to abstract mathematical ideas to help them realize their aesthetic ambitions. Man Ray, Marcel Duchamp, and, perhaps most famously, Piet Mondrian used principles of mathematics in their work. Was it mere coincidence, or were these artists simply following their instincts, which in turn were ruled by mathematical underpinnings, such as optimal solutions for filling a space? If math exists within visual art, can it be found within literary pursuits? In short, just what is the relationship between mathematics and the creative arts? In this provocative, original exploration of mathematical ideas in art and literature, Robert Tubbs argues that the links are much stronger than previously imagined and exceed both coincidence and commonality of purpose. In the end, Tubbs makes the case that art can be better appreciated when the math that inspired it is better understood.

Table of Contents

'Mathematics in Twentieth-Century Literature and Art' cover image
Mathematics in Twentieth-Century Literature and Art

Robert Tubbs

During the twentieth century, many artists and writers turned to abstract mathematical ideas to help them realize their aesthetic ambitions. Man Ray, Marcel Duchamp, and, perhaps most famously, Piet Mondrian used principles of mathematics in their work. Was it mere coincidence, or were these artists simply following their instincts, which in turn were ruled by mathematical underpinnings, such as optimal solutions for filling a space? If math exists within visual art, can it be found within literary pursuits? In short, just what is the relationship between mathematics and the creative arts? In this provocative, original exploration of mathematical ideas in art and literature, Robert Tubbs argues that the links are much stronger than previously imagined and exceed both coincidence and commonality of purpose. In the end, Tubbs makes the case that art can be better appreciated when the math that inspired it is better understood.

Table of Contents