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Euclidean & Non-Euclidean Geometries: Development and History
Euclidean & Non-Euclidean Geometries: Development and History

This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high...

Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus has a deservedly central role in higher education. It is not only the key to the full range of scientific and engineering disciplines; it is also a crucial component in a student’s intellectual development. I hope my text will help to open up this multifaceted world of ideas for the student. Like a great...
Gravitation (Physics Series)
Gravitation (Physics Series)
This is a textbook on gravitation physics (Einstein's "general relativity" or "geometrodynamics"). It supplies two tracks through the subject. The first track is focused on the key physical ideas. It assumes, as mathematical prerequisite, only vector analysis and simple partial-differential equations. It is suitable for a...
Linear Algebra: A Geometric Approach
Linear Algebra: A Geometric Approach
One of the most enticing aspects of mathematics, we have found, is the interplay of ideas from seemingly disparate disciplines of the subject. Linear algebra provides a beautiful illustration of this, in that it is by nature both algebraic and geometric. ...
Calculus
Calculus

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Mathematical Structures for Computer Science
Mathematical Structures for Computer Science
Discrete structures plays an ever more prominent role in computer science education. Computing Curricula 2001 (CC2001) was a joint undertaking of the Institute for Electrical and Electronic Engineers/Computer Society (IEEE/CS) and the Association for Computing Machinery (ACM). The final report may be found at...
Calculus Second Edition
Calculus Second Edition
On Teaching Mathematics

As a young instructor, I enjoyed teaching but I didn’t appreciate how difficult it is to communicate mathematics effectively. Early in my teaching career, I was confronted with a student rebellion when my efforts to explain epsilon-delta proofs were not greeted with the enthusiasm I
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Computers and Intractability: A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences)
Computers and Intractability: A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences)

Few technical lerms have gained such rapid notoriety as the appela tion "NP-complete." In the short lime since its introduction in the early 1970's, this term has come to symbolize the abyss of inherent intractability that algorithm designers increasingly face as they seek to solve larger and more complex problems. A...

Mathematical Structures for Computer Science: A Modern Treatment of Discrete Mathematics
Mathematical Structures for Computer Science: A Modern Treatment of Discrete Mathematics

The important role that discrete structures plays in computer science is gaining recognition. Computing Curricula 2001 (CC2001), the latest curriculum recommendation for computer- related education, was a joint undertaking of the Institute for Electrical and Electronic Engineers/Computer Society (IEEE/CS) and the Association for...

Computer Algorithms
Computer Algorithms

If wo try to identify those contributions of computer science which will be long lasting, surely one of these will be the refinement of the concept called algorithm. Ever since man invented the idea of a machine which could per form basic mathematical operations, the study of what can be computed and how it can be done well was...

The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
Science is inextricably linked with mathematics. Statistician David Salsburg examines the development of ever-more-powerful statistical methods for determining scientific truth in The Lady Tasting Tea, a series of historical and biographical sketches that illuminate without alienating the mathematically timid. Salsburg, who has worked...
The Fractal Geometry of Nature
The Fractal Geometry of Nature
Imagine an equilateral triangle. Now, imagine smaller equilateral triangles perched in the center of each side of the original triangle--you have a Star of David. Now, place still smaller equilateral triangles in the center of each of the star's 12 sides. Repeat this process infinitely and you have a Koch snowflake, a mind-bending geometric...
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