Mathematics

By Cao Minh Quang.

Best mathematics books

Calculus and Its Origins (Spectrum)

Calculus & Its Origins is an outline of calculus as an highbrow pursuit having a 2,000-year history.

Author David Perkins examines the level to which mathematicians and students from Egypt, Persia, and India absorbed and nourished Greek geometry, and info how the students wove their inquiries right into a unified theory.

Chapters conceal the tale of Archimedes discovery of the realm of a parabolic phase; ibn Al-Haytham s calculation of the quantity of a revolved zone; Jyesthadeva s clarification of the endless sequence for sine and cosine; Wallis s deduction of the hyperlink among hyperbolas and logarithms; Newton s generalization of the binomial theorem; Leibniz s discovery of integration by way of parts--and a lot more.

Each bankruptcy additionally includes workouts through such mathematical luminaries as Pascal, Maclaurin, Barrow, Cauchy, and Euler. Requiring just a uncomplicated wisdom of geometry and algebra--similar triangles, polynomials, factoring--and a willingness to regard the endless as metaphor--Calculus & Its Origins is a treasure of the human mind, pearls strung jointly through mathematicians throughout cultures and centuries.

Nonmeasurable Sets and Functions

The booklet is dedicated to numerous buildings of units that are nonmeasurable with recognize to invariant (more usually, quasi-invariant) measures. Our start line is the classical Vitali theorem declaring the lifestyles of subsets of the genuine line which aren't measurable within the Lebesgue feel. This theorem prompted the improvement of the subsequent attention-grabbing subject matters in arithmetic: 1.

Extra info for Best problems from around the world - mathematical olympiads

Sample text

B) The digits of a natural number are rearranged and the resultant number is added to the original number to give 1010. Prove that the original number was divisible by 10. 3. Four lighthouses are arbitarily placed in the plane. Each has a stationary lamp which illuminates an angle of 90 degrees. Prove that the lamps can be rotated so that at least one lamp is visible from every point of the plane. 4. (a) Can you arrange the numbers 0, 1, ... , 9 on the circumference of a circle, so that the difference between every pair of adjacent numbers is 3, 4 or 5?

One vertex of a rhombus lies on side AB, another on side BC, and a third on side AD. Find the area of the set of all possible locations for the fourth vertex of the rhombus. 10. A natural number k has the property that if k divides n, then the number obtained from n by reversing the order of its digits is also divisible by k. Prove that k is a divisor of 99. 60 ☺ The best problems from around the world Cao Minh Quang 2nd ASU 1968 problems 1. An octagon has equal angles. The lengths of the sides are all integers.

Show that you can form a sum s = b1a1 + ... + bnan with each bi +1 or -1, so that 0 ≤ s ≤ a1. 7. Prove that you can always draw a circle radius A/P inside a convex polygon with area A and perimeter P. 8. A graph has at least three vertices. Given any three vertices A, B, C of the graph we can find a path from A to B which does not go through C. Prove that we can find two disjoint paths from A to B. [A graph is a finite set of vertices such that each pair of distinct vertices has either zero or one edges joining the vertices.