sets relations and functions

Sets, Relations and Functions#

a set is many that allows itself to be thought of as a one

— Cantor

1.1 Introduction#

The concepts of sets, relations and functions occupy a fundamental place in the mainstream of mathematical thinking. As rightly …

basic algebra

Basic Algebra#

I see it but I don’t believe it.

— Richard Dedekind

2.1 Introduction#

Algebra is a branch of mathematics in which one expresses relations among quantities by using symbols to represent these quantities. The symbols are called the …

trigonometry

Chapter 3: Trigonometry#

3.1 Introduction#

Trigonometry is primarily a branch of Mathematics that studies relationship involving sides and angles of triangles. The word trigonometry stems from the Greek word trigonon which means triangle and metron …

combinatorics and mathematical induction

Combinatorics and Mathematical Induction#

No great discovery was ever made without a bold guess

— Newton

4.1 Introduction#

Combinatorics is the branch of mathematics which is related to counting. It deals with arrangements of objects as well as …

combinatorics and mathematical induction

Chapter 5: Binomial Theorem, Sequences and Series#

5.1 Introduction#

Binomial theorem facilitates the algebraic expansion of the binomial \( (a + b) \) for a positive integral exponent \( n \). Binomial theorem is used in all branches of Mathematics …

two-dimensional-analytical-geometry

Two Dimensional Analytical Geometry#

“My powers are ordinary. Only my application brings me success”.

— Sir Isaac Newton

6.1 Introduction#

Francois Viète (1540-1603) introduced the first systematic algebraic notation and contributed to …

matrices and determinants

Chapter 7: Matrices and Determinants#

7.1 Introduction#

The beginnings of matrices and determinants go back to the second century BC although traces can be seen back to the fourth century BC. However, it was not until near the end of the seventeenth …

vector algebra

Vector Algebra#

“On earth there is nothing great but man; In man there is nothing great but mind”

— Hamilton

8.1 Introduction#

A pilot constructing a flight plan has to be concerned about the plane’s course, heading, air speed, and …

differential calculus limits and continuity

Chapter 9: Limits and Continuity#

9.1 Introduction#

Calculus is about rates of change. Rates of change occur in all the sciences. A mathematician is interested in measuring the rate of change of the deviations of a straight line at a point on a curve, …

differential calculus differentiability and methods of differentiation

Differentiability and Methods of Differentiation#

10.1 Introduction#

In this chapter we discuss the concept of derivative and related concepts and develop tools necessary for solving real life problems. In this connection, let us look at the following …

integral calculus

11. Integral Calculus#

11.1 Introduction#

Gottfried Wilhelm Leibniz (1646-1716) and Sir Isaac Newton (1643-1727) independently discovered calculus in the mid-17th century. Leibniz, a German philosopher, mathematician, and political adviser, importantly …

introduction to probability theory

Chapter 12: Introduction to Probability Theory#

12.1 Introduction#

The most important questions of life are, indeed, for the most part, really only problems of probability – Pierre-Simon Laplace

A gambler’s dispute in 1654 led to the creation of …