Wk 1: Tues9/3 : . Course management details, syllabus. Outline of topics for the semester. Worksheet on sequences using Excel.
Thur 9/5: Sequences via iteration, chaos, notion of a limit, group project on sequences.
Wk 2: Tues 9/10: Sets, functions, 1-1, onto, domain, range (Sect 1.2)
Thur 9/12: Presentations on types of sequences. Absolute value and its properties (an example of a Norm). Sect 1.1.
Wk 3: Tues 9/ 17: Cardinality (Sect 1.3), countable, uncountable
Thur 9/ 19: More on cardinality, 3 properties of an equivalence relation,
Wk 4: Tues 9/23: The logic of proofs (Sect 1.4), Formal definition of limit of a sequence (Sect 2.1)
Thur 9/26: Worksheet on limits
Wk 5: Tues 10/1: Sect 2.1: more examples of limits, diverging to infinity.
Thur 10/3: Sect 2.2: limit laws (addition, multiplication, boundness). Quiz 3 handed out.
Wk 6: Tues 10/10: Sect. 5.6 Metric Spaces, Sect 2.3:Squeeze Law
Thur 10/12: Sect 2.4 Cauchy sequences, Completeness
Wk 7: fall break
Wk 8: Tues 10/22 Sect 2.5 Sup and Inf
Thur 10/24 Sect 2.6 Bolzano-Weierstrass Theorem
Wk 9: Tues 10/29 Review for Mid-term
Thur 10/31
Wk 10: Tue 11/ 5 Sect 3.1: Continuity of functions via sequence defintion
Thur 11/7 Sect. 3.1: Continuity with d-e condition
Wk 11: Tues 11/12 Sect 3.2 Uniform Convergence
Thur 11/14: Sect 3.3. The Riemann Integral. Mathematica Notebook.
Wk 12: Tues 11/14: Student presentations on Sect. 3.2