MATH 3001

SYLLABUS AND HOMEWORK

Mathematics 3001

Analysis 1

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Homework is due in class and must be stapled, with your name on it, to receive credit.

You may find the Mathematics Help Room (MATH 175) to be useful as a meeting point for discussing homework.

Date	Topics covered	Reading	Homework Assignments
Monday August 26	Class Introduction Sec 1-7: Review of background material	Read Chapters 1 and 2
Wednesday August 28	Sec 1-7: Review (Cont.)	Read Section 8 (especially Theorem 8.10, and work through Example 8.11)
Friday August 30	Sec 8: Cardinality	Read Section 10	HW 1: Due Friday August 30 Sec 5: 5.1 (a), (d), 5.2 (a-c), 5.3-5.7, 5.8, 5.19-26 Sec 6: 6.2, 6.3, 6.4, 6.8-17 Recommended, but do NOT turn in: Sec 1: 1.2, 1.3, 1.7, 1.8, 1.14 Sec 2: 2.3, 2.5, 2.9, 2.13, 2.14 Sec 3: 3.3, 3.4, 3.5, 3.6 Sec 4: 4.1-5, 4.19, 4.20
Monday September 2	NO CLASS	LABOR DAY	NO CLASS
Wednesday September 4	Sec 10: Natural numbers and induction	Read Section 11 (especially familiarize yourself with the axioms of an ordered field, and work through Practice Problems 11.2 and 11.3.)
Friday September 6	Sec 11: Ordered Fields		HW 2: Due Friday September 6 Sec 7: 7.1-33 odd (except for 7.3, 7.7, 7.9) Sec 8: 8.1, 8.7, 8.16, 8.18 (except for 8.1(d))
Monday September 9	Sec 12: The Completeness Axiom	Read Section 12
Wednesday September 11	Construction of the real numbers	Read Section 13
Friday September 13	NO CLASS	CAMPUS CLOSED	NO CLASS
Monday September 16	Sec 13: Topology of the real numbers
Wednesday September 18	Topological spaces	Read Section 14
Friday September 20	Continuous maps, and metric spaces		HW 3: Due Friday September 20 Sec 8: 8.19-23 Sec 10: 10.1-16, 10.19, 10.21, 10.22, 10.28.
Monday September 23	Sec 14: Compact subsets of the real numbers, compact and connected topological spaces	Read Section 16 (you must understand Definition 16.2)
Wednesday September 25	Sec 16: Convergence for sequences.	Read Section 17
Friday September 27	Sec 16: Convergence for sequences (cont.)		HW 4: Due Friday September 27 Sec 7: 7.3, 7.7, 7.9 Sec 8: 8.2, 8.3, 8.9, Sec 11: 11.1, 11.2, 11.3(c)(f)(h)(j)(k), 11.5, 11.7, 11.10, 11.11, 11.12 Sec 12: 12.1, 12.2, 12.6, 12.7
Monday September 30	Homework review
Wednesday October 2	Review
Friday October 4	MIDTERM I		Practice exam .pdf
Monday October 7	Sec 17: Limit theorems for sequences
Wednesday October 9	Sec 17: Limit theorems for sequences (cont.)	Read Section 18
Friday October 11	Sec 18: Monotone sequences and Cauchy sequences	Read Section 19	HW 5: Due Friday October 11 Sec 12: 12.10, 12.12, 12.14, 12.15 Sec 13: 13.1, 13.2, 13.3, 13.4, 13.11, 13.15, 13.20 Sec 14: 14.1, 14.2, 14.3, 14.5(a), 14.6
Monday October 14	Sec 18: Monotone sequences and Cauchy sequences (Cont.)
Wednesday October 16	Sec 19: Subsequences
Friday October 18	Sec 19: Subsequences (cont.)	Read Section 20	HW 6: Due Friday October 18 Sec 16: 16.1, 16.2, 16.4, 16.5, 16.6(b)(d)(e), 16.7(a)(f), 16.8(c), 16.11, 16.15
Monday October 21	Sec 20: Limits of functions
Wednesday October 23	Sec 20: Limits of functions (cont.)	Read Section 21 (work through the proof of Theorem 21.14)
Friday October 25	Sec 21: Continuous functions	Read Section 22 (work through examples 22.7 and 22.8)
Monday October 28	Sec 21: Continuous functions (cont.)		HW 7: Due Monday October 28 Sec 17: 17.1, 17.2, 17.3, 17.6, 17.8, 17.15(a) Sec 18: 18.1, 18.2, 18.3(a), 18.4, 18.7, 18.14, 18.15
Wednesday October 30	Sec 22: Properties of continuous functions	Read Section 23
Friday November 1	Sec 23: Uniform continuity	Read Section 25 (you must understand Definition 25.1, work through Examples 25.2 and 25.4, and do Practice Problem 25.5)	HW 8: Due Friday November 8 Sec 19: 19.1, 19.2, 19.5(a)(d)(f), 19.11, 19.12, 19.13 Sec 20: 20.1, 20.2, 20.4, 20.5, 20.7, 20.14, 20.16, 20.18
Monday November 4	Homework review
Wednesday November 6	Review
Friday November 8	MIDTERM II		Practice exam .pdf
Monday November 11	Sec 25: The Derivative
Wednesday November 13	Sec 25: The Derivative (cont.)	Read Section 26 (especially Example 26.4 and do Practice Problem 26.5)
Friday November 15	Sec 26: The Mean Value Theorem	Read Section 29	HW 9: Due Friday November 15 Sec 21: 21.1, 21.2, 21.3, 21.6(c)(d)(f), 21.11 Sec 22: 22.1, 22.2, 22.3(a)(b)(e), 22.5, 22.7, 22.13
Monday November 18	Sec 29: The Riemann Integral
Wednesday November 20	Sec 29: The Riemann Integral (cont.)	Read Section 30
Friday November 22	Sec 30: Properties of the Riemann Integral	Read Section 31	HW 10: Due Friday November 22 Sec 23: 23.1, 23.2, 23.3(d)(e), 23.5 Sec 25: 25.1, 25.2, 25.5
Monday November 25 - Friday November 29	NO CLASS	THANKSGIVING BREAK	NO CLASS
Monday December 2	Sec 31: The Fundamental Theorem of Calculus
Wednesday December 4	Further topics
Friday December 6	Further topics		HW 11: Due Friday December 6 Sec 25: 25.6, 25.7(d), 25.8, 25.11, 25.15 Sec 26: 26.1, 26.2, 26.6, 26.10, 26.11, 26.15
Monday December 9	Further topics
Wednesday December 11	Homework review
Friday December 13	Review		HW 12: Due Friday December 13 (Not for credit, do not turn in) Sec 29: 29.1, 29.2, 29.5, 29.7, 29.8, 29.9, 29.11, 29.13, 29.16 Sec 30: 30.1, 30.2, 30.3, 30.9, 30.11, 30.12, 30.15, 30.21 Sec 31: 31.1, 31.2, 31.4, 31.5, 31.12, 31.13
Saturday December 14	FINAL EXAM DUAN G131 7:30-10:00 PM	FINAL EXAM	Practice exam .pdf

For those of you typing up your homework, you may want to consider learning to use LaTex. If you have a mac, one possible easy way to get started is with texshop. If you are using linux, there are a number of other possible ways to go, using emacs, ghostview, etc. If you are using windows, you're on your own, but I'm sure there's something online. Here is a sample homework file to use: (the .tex file, the .bib file, and the .pdf file). It is probably easiest to just look at the .tex file, and start to experiment. There is also the (Not so) short introduction to latex, which will answer most of your questions (although typing your question into your favorite search engine will probably work well, too). You may also want to try http://scribtex.com/ for a cloud version.