Weekly Breakdown:
[Week 1] Sets, Properties of sets, Relations, and their types, Equivalence relation, and partitions.
[Week 2] Algebra on Z_n, Functions, and their types.
[Week 3] Mathematical induction, Finite, and Infinite sets.
Assignment 1
Quiz 1 , Quiz 1 Solution
[Week 4] Countable sets, Cantor's theorem, Real numbers system, Completeness of R.
[Week 5] Sequences, Basic properties, Monotone sequences.
[Week 6] Bounded sequences, Subsequences, Bolzano Weirstrass Theorem.
[Week 7] Nested Intervals Theorem, Cauchy sequences, Completeness Axioms.
Midterm Exam
Midterm Solutions
[Week 8] Series, Partial sums, Cauchy criteria, Convergence Tests, Absolute and conditional convergence.
[Week 9] Cluster points, Limit of a function at a cluster point, Limit Laws, Sequential criteria for limits.
[Week 10] Continuous functions, Sequential criteria, Basic laws of continuity.
[Week 11] Composition of continuous functions, Continuous functions on compact intervals, Extreme values theorem.
[Week 12] Derivative of a function at a point, Laws of differentiation, Caratheodory's theorem.
[Week 13] Critical points, First derivative test, monotonicity and derivatives, monotone inverse theorem.
[Week 14] Mean value theorem and applications, L'Hopital Rule and Taylor's theorem.
Final Exam
Final Exam Key