******WRITTEN ACCORDING TO TIFR GS MATH ENTRANCE EXAM PATTERN ******ALL SECTIONS ARE THOROUGHLY EXPLAINED WITH AMPLE SHORT AND LONG QUESTIONS WITH THEIR ANSWERS AND EXPLANATIONS AS WELL. ******20 MODEL PAPERS THOROUGHLY SOLVED. ******COMPLETE TOPIC WISE EXPLANANTION ACCORDING TO TIFR GS MATH ******THEORY AND PRACTISE EXAMPLES ARE ALSO INCLUDED SOLUTIONS OF PART - I & PART - II BOTH SECTIONS ******TOPICS COVERED ARE ****ALGEBRA: DEFINITIONS AND EXAMPLES OF GROUP (FINITE AND INFINITE, COMMUTATIVE AND NON-COMMUTATIVE), CYCLIC GROUPS, SUBGROUPS, HOMOMORPHISMS, QUOTIENTS. DEFINITIONS AND EXAMPLE OF RINGS AND FIELDS. BASIC FACTS ABOUT ****FINITE DIMENSIONAL VECTOR SPACES, MATRICES, ****DETERMINANTS, AND RANKS OF LINEAR TRANSFORMATIONS. INTEGERS AND THEIR BASIC PROPERTIES. ****POLYNOMIALS WITH REAL OR COMPLEX COEFFICIENTS IN 1 VARIABLE. ****ANALYSIS: BASIC FACTS ABOUT REAL AND COMPLEX NUMBERS, CONVERGENCE OF SEQUENCES AND SERIES OF REAL AND COMPLEX NUMBERS, CONTINUITY, DIFFERENTIABILITY AND RIEMANN INTEGRATION OF REAL VALUED FUNCTIONS DEFINED ON AN INTERVAL (FINITE OR INFINITE), ****ELEMENTARY FUNCTIONS (POLYNOMIAL FUNCTIONS, RATIONAL FUNCTIONS, EXPONENTIAL AND LOG, TRIGONOMETRIC FUNCTIONS). ****GEOMETRY/TOPOLOGY: ELEMENTARY GEOMETRIC PROPERTIES OF COMMON SHAPES AND FIGURES IN 2 AND 3 DIMENSIONAL EUCLIDEAN SPACES (E.G. TRIANGLES, CIRCLES, DISCS, SPHERES, ETC.). ****PLANE ANALYTIC GEOMETRY (= COORDINATE GEOMETRY) AND TRIGONOMETRY. ****DEFINITION AND BASIC PROPERTIES OF METRIC SPACES, EXAMPLES OF SUBSET EUCLIDEAN SPACES (OF ANY DIMENSION), CONNECTEDNESS, COMPACTNESS. CONVERGENCE IN METRIC SPACES, CONTINUITY OF FUNCTIONS BETWEEN METRIC SPACES. ****GENERAL: PIGEON-HOLE PRINCIPLE (BOX PRINCIPLE), INDUCTION, ELEMENTARY PROPERTIES OF DIVISIBILITY, ELEMENTARY COMBINATORICS (PERMUTATIONS AND COMBINATIONS, BINOMIAL COEFFICIENTS), ****ELEMENTARY REASONING WITH GRAPHS.