Cheenta
Passion for Mathematical Science
Book List
If you are starting with the course, then you may buy the books in the Miscellaneous
Section only. Later, your faculty will prescribe other books in class.
Miscellaneous
● Challenges and Thrills of Pre-College Mathematics by Venkatchala
● Excursion in Mathematics by Bhaskaracharya Pratishthana
● Test of Mathematics at 10+2 Level by East West Press
Number Theory
● Excursion in Mathematics; Challenges and Thrills of Pre-College
Mathematics
● Elementary Number Theory by David Burton
Combinatorics
● Principles and Techniques in Combinatorics by Chen Chuan Chong and
Koh Khee Meng
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Algebra
● Excursion in Mathematics; Challenges and Thrills of Pre-College
Mathematics
Geometry
● Challenges and Thrills of Pre-College Mathematics
Trigonometry
● Trigonometry by S.L. Loney
● 101 Problems in Trigonometry by Titu Andreescu
Inequality
● Inequality by Little Mathematical Library
Complex Numbers
● Complex Numbers from A to Z
Coordinate Geometry
● Coordinate Geometry by S.L. Loney
Calculus
● Pre-Calculus by Tarasov
● Single Variable Calculus by I.A. Maron
● Play with Graphs (Arihant Publication)
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Curriculum
Number Theory I
This is the first course in elementary number theory:
● NT.I.1Primes, Divisibility
● NT.I.2Arithmetic of Remainders
● NT.I.3 Bezout's Theorem and Euclidean Algorithm
● NT.I.4Theory of congruence
● NT.I.5Number Theoretic Functions
● NT.I.6Theorems of Fermat, Euler, and Wilson
● NT.I.7Pythagorean Triples
● NT.I.8Chinese Remainder Theorem
Combinatorics I
This is the first course in combinatorics and elementary counting techniques:
● Com.I.1 Multiplication and Addition rules
● Com.I.2 Bijection Principles
● Com.I.3Combinatorial Coefficients
● Com.I.4Inclusion and Exclusion Principles
● Com.I.5Pigeon Hole Principle
● Com.I.6Recursions
● Com.I.7 Shortest Route Problems
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Algebra I
This is a first course is school algebra. (We assume that the student is familiar with
algebraic expressions, and elementary algebraic identities)
● Alg.I.1Algebraic identities (Sophie Germain, Cube of three etc.)
● Alg.I.2Mathematical Induction
● Alg.I.3 Binomial Theorem
● Alg.I.4Linear Equations
● Alg.I.5Quadratic Equation
● Alg.I.6Remainder Theorem
● Alg.I.7Theorems related to roots of an integer polynomial
Geometry I
● Geo.I.1Locus visualization
● Geo.I.2Straight Lines
● Geo.I.3Triangles
● Geo.I.4Geometric Constructions
● Geo.I.5Circles
Trigonometry I
● Trig.I.1Angle and rotation
● Trig.I.2Half arcs and Half chords - Genesis of trigonometric ratios
● Trig.I.3Elementary ratios and associated angles
● Trig.I.4Trigonometric identities
● Trig.I.5Geometry and trigonometry
● Trig.I.6Basic properties of Triangles
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● Trig.I.7Compound Angles
● Trig.I.8 M
ultiple and Submultiple Angles
● Trig.I.9Trigonometric Series
● Trig.I.10Height and Distance
Inequality I
This first course in inequality must be preceded by a basic course in algebra.
● Ineq.I.1Geometric Inequalities
● Ineq.I.2Arithmetic and Geometric Mean Inequality
● Ineq.I.3Cauchy Schwarze Inequality
● Ineq.I.4 T
itu's Lemma
Complex Number I
● Complex.I.1Geometry of Screw Similarity
● Complex.I.2Field Properties of complex Number
● Complex.I.3nth roots of unity and Primitive roots
● Complex.I.4 Basic applications to geometry
Calculus I
● Calc.I.1Sequences and Series
● Calc.I.2Limit
● Calc.I.3Functions
● Calc.I.4Continuity
● Calc.I.5Differential Calculus
● Calc.I.6Cauchy's Theorem and Mean value
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● Calc.I.7Graphing Techniques
● Calc.I.8Integral Calculus
Coordinate Geometry I
● CG.I.1Straight Lines
● CG.I.2Circles
● CG.I.3Parabola
● CG.I.4Ellipse
● CG.I.5 Hyperbola
● CG.I.6Polar loci
