Math Unlimited | Essays in Mathematics | R. Sujatha, H. N. Ramaswamy,

Book

ABSTRACT

This collection of essays spans pure and applied mathematics. Readers interested in mathematical research and historical aspects of mathematics will appreciate the enlightening content of the material. Highlighting the pervasive nature of mathematics today in a host of different areas, the book also covers the spread of mathematical ideas and techn

TABLE OF CONTENTS

part |2 pages

Part I: Mathematics for its Own Sake

chapter 1|15 pages

Group Theory—What’s Beyond

chapter 3|5 pages

Modular group -an arithmetic group

chapter 2|18 pages

Splitting Primes

chapter 3|16 pages

Elliptic Curves and Number Theory

chapter 4|8 pages

Curvature and Relativity

chapter 7|2 pages

Curvature and relativity

chapter 5|7 pages

Generating Functions

chapter |3 pages

Weil Conjectures

chapter 6|22 pages

Approximating Continuous Functions by Polynomials

part |2 pages

Part II: Applicable Mathematics

chapter 7|25 pages

The Wonderful World of Eigenvalues

chapter |3 pages

References

chapter 8|10 pages

On Pták’s Nondiscrete Induction

chapter |2 pages

References

chapter 9|6 pages

Partial Differential Equations

chapter |2 pages

References

chapter 10|4 pages

Large Deviations

chapter 4|8 pages

Cramér’s Theorem

chapter 11|17 pages

From the Binary Alphabet to Quantum Computation

chapter |1 pages

References

chapter 12|12 pages

Is There a Science Behind Opinion Polls?

chapter 13|30 pages

An Introduction to Financial Mathematics

chapter |2 pages

References

part |2 pages

Part III: Mathematics and Computer Science

chapter 14|14 pages

Linear Time, Almost Linear Time, and Almost Always Linear Time: Snippets from the Work of Robert Endre Tarjan

chapter 15|20 pages

Group Representations and Algorithmic Complexity

chapter |2 pages

References

chapter 16|20 pages

Regular Languages: From Automata to Logic and Back

part |2 pages

Part IV: Mathematics and Physics

chapter 17|2 pages

Variational Calculus in Mathematics and Physics

chapter 2|8 pages

Variational Problems

chapter 18|1 pages

The Forces of Nature

chapter 2|5 pages

The principle of least action

chapter 19|14 pages

The Reciprocal Interaction Between Mathematics and Natural Law

part |2 pages

Part V: Mathematics and Biology

chapter 20|18 pages

An Introduction to Mathematical Biology

chapter 21|20 pages

Mathematics and Biology: The Growing Synergy

chapter 22|18 pages

Mathematical Biology: A Modelling Approach

chapter 6|4 pages

Classiﬁcation of Mathematical Models

chapter 23|23 pages

A Mathematical Approach to Brain and Cognition

chapter 5|1 pages

Conclusions

chapter |2 pages

References

part |2 pages

Part VI: Mathematics over the Millenia

chapter 24|16 pages

Rational Quadrilaterals from Brahmagupta to Kummer

chapter 25|3 pages

Magic Squares

chapter 3|5 pages

Na¯ra¯yan . a Pan . d . ita’s 4 × 4 pan-diagonal magic squares

chapter 5|4 pages

Na¯ra¯yan . a Pan . d . ita’s “folding” method for odd order magic squares

chapter 26|20 pages

Differences in Style, but not in Substance: Ancient Indian Study of Combinatorial Methods

chapter 27|12 pages

In Square Circle: Geometric Knowledge of the Indus Civilization

chapter |12 pages

Color Plate Section

chapter |1 pages

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