MA361 Fall 2009 Syllabus

Topic NumberTopicText SectionSubtopics
1 Preliminaries N/AReview of Symbolic Logic
N/AOverview of Proofs
N/AOverview of LaTeX
2 The Real Number System 1.1Definitions and Notation
1.2The Field Axioms
The Order Axioms
1.3The Completeness Axiom and its Implications
1.4The Well-Ordering Principle and Mathematical Induction
1.5Inverse Functions and Images
1.6Countable and Uncountable Sets
3 Sequences of Real Numbers 2.1 The Limit of a Sequence
2.2Some Limit Theorems
2.3The Bolzano-Weierstrass Theorem
2.4Cauchy Sequences
2.5Limits Supremum and Infimum
4 Functions Defined on the Set of Real Numbers 3.1 Two-Sided Limits
3.2One-Sided Limits
Limits at Infinity
3.3Continuity
3.4Uniform Continuity
5 The Basic Topology of R N/AThe Cantor Set
N/AOpen and Closed Sets
N/ACompact Sets
N/APerfect Sets and Connected Sets
N/ABaire's Theorem
6 Differentiability on R 4.1 The Derivative
4.2Differentiability Theorems
4.3The Mean Value Theorem
4.4Taylor's Theorem and L'Hospital's Rule
7 Integrability on R 5.1 The Riemann Integral
5.2Riemann Sums
5.3The Fundmental Theorem of Calculus
5.4Improper Riemann Integration