Portal through Mathematics: Journey to Advanced Thinking (Anneli Lax New Mathematical Library)

Cover
Title Page
Contents
Foreword
Preface for an American Readership
Author's Preface
Part I
1. Surprising right triangles
2. Surprisingly short
solutions of geometric
problems
3. A natural assertion with a
surprising proof
4. Surprising answers
5. A surprising connection
between three sequences
Part II
Algebra, Calculus, and
Geometry: problems
6. Five problems and
a function
7. Five solutions of a
routine problem
8. Equations of the form
f (x, y) = g(x, y) and their
generalizations
9. The generalized version of
Viete’s formula
10. Multiple roots of
polynomials
11. 
Non-routine applications
of the derivative
12. 
Complex numbers,
polynomials, and
trigonometry
13. 
Complex numbers and
geometry
14. Areas of triangles and quadrilaterals
15.
Constructions in solid
geometry
16.
Inequalities
17. Diophantine equations
18. Combinatorial tales
19. Integrals
Part III. Algebra, Calculus, and
Geometry: theory
(a little way beyond high
school mathematics)
20. Functional equations of
elementary functions
21. Sequences given by
recurrence relations
22. The “golden ratio” or
solving equations of the
form f(x) = x
23. Convex functions:
inequalities and
approximations
24. Taylor’s formula, Euler’s
formula, and a
combinatorial problem
25. Derivatives of
vector-functions
26. Polynomials and
trigonometric relations
27. Areas and volumes as
functions of co-ordinates
28. Values of trigonometric
functions and sequences
satisfying a certain
recurrence relation
29. Do there exist further
“numbers” beyond
complex numbers?
Solutions of the
supplementary problems
Index
Back Cover