As you are looking for syllabus of B.SC Mathematics CBCS System Program of Mumbai University, so here I am providing complete syllabus:

Mumbai University B.SC Mathematics CBCS System Program Syllabus
Semester I
Calculus I - USMT101,UAMT101
Unit I Real Number system
Unit II Sequences
Unit III Limits & Continuity
Algebra I - USMT102
Unit I Integers & divisibility
Unit II Functions & Equivalence relation
Unit III Polynomials

Semester II
Calculus II - USMT201,UAMT201
Unit I Series
Unit II Continuous functions & Differentiation
Unit III Applications of differentiation
Linear Algebra - USMT202
Unit I System of Linear Equations & Matrices
Unit II Vector spaces
Unit III Basis & Linear transformations

USMT101/UAMT101 CALCULUS I
Unit I: Real Number System (15 Lectures)
Real number system R and order properties of R, Absolute value |.| and its
properties.
AM-GM inequality, Cauchy-Schwarz inequality, Intervals and neighbourhoods,
Hausdorff property.
Bounded sets, statement of l.u.b. axiom, g.l.b. axiom and its consequences,
Supremum and infimum, Maximum and minimum, Archimedean property and
its applications, density of rationals.
Unit II: Sequences (15 Lectures)
Definition of a sequence and examples, Convergence of sequence, every convergent
sequence is bounded, Limit of a convergent sequence and uniqueness of
limit , Divergent sequences.
algebra of convergent sequences, sandwich theorem, monotone sequences, monotone
convergence theorem and consequences such as convergence of (1 + 1 n ) n ).
Definition of subsequence, subsequence of a convergent sequence is convergent
and converges to the same limit, definition of a Cauchy sequence, every
convergent sequence is a Cauchy sequence and converse.
Unit III: Limits & Continuity (15 Lectures)
Brief review: Domain and range of a function, injective function, surjective function,
bijective function , composite of two functions (when defined), Inverse of
a bijective function.

Mumbai University B.SC Mathematics CBCS System Program Syllabus

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