Math 2283, Spr 2008, Professor D. Hejhal This page will be used for general announcements and the homework listing. ------------------------------------------------------------------------------- Office Hours (Currently): M,W 14:15-15:00 **SPECIAL OFFICE HOUR FRIDAY MAY 16, 15:15-16:00. ------------------------------------------------------------------------------ FINAL EXAM Official time May 17, Sat, 4-6pm Ford Hall 130 Early Version May 12, Monday, 12:20-2:20pm Ford Hall **150** (just next to our normal room) ------------------------------------------------------------------------------ LATEST HOMEWORK : (official due date of homework from week N is THURSDAY of week N+1 ) assigned problem numbers ----------------------------------------------------------- week 1 chap 1 4.5,4.6,4.7 (rec: 4.4,4.10,4.11) week 2 chap 1 4.16, 4.22 (rec: 4.17, 4.20, 4.21, 4.23) Let E and F be subsets of the reals R. Prove that R-(E intersects F) = (R-E) union (R-F). chap 2 1.8 (rec: 1.7, 1.9,1.10,1.12) week 3 chap 2 2.8,2.11,2.12, 2.17 (rec: 2.9,2.10,2.13,2.14) hejhal prob: Find a 1-1 correspondence between R and the closed interval [0,1]. chap 3 1.18, 1.20, 1.21 (rec: rest of 1.17--1.25) week 4 chap 3 2.10, 2.12, 2.14(using theorems), 2.15 rec: 2.11,2.13 3.7, 4.4(cd), 4.5(b through i) week 5 chap 3 5.6, 6.8, 6.9, 6.10 (rec: 6.7, 6.11 with c > 0) week 6 chap 3 6.15(a) (use x*x - 7, etc), 6.25(use 6.24c or DH's handout) week 7 chap 4 1.12 (d-ell) (conv or divergent?? find value if easy!) week 8 chap 4 2.20, 3.5(cd) chap 4 5.12(acdgnors) using 2.5 or integral test (remember that the extended comparison test applies to improper integrals -- this can simplify matters) chap 4 5.12(bj) using 4.1 (comparison test) and p-series week 9 chap 4 5.12(fpqw) using ratio or root test chap 4 5.12(vyz) using any method chap 4 6.15(ef) WITHOUT USING ALT SERIES TEST week 10 chap 4 6.15(aci), 6.12(the series is 1/e), 6.13(series is cos 1) [in 6.15, remember to specify your 'k' if you use alt series test only starting at n=k] chap 4 7.8(bcdhk) week 11 chap 4 8.17(bc), 8.18(abc) recommended: 7.8(eijl), 7.9, 7.11, 7.12 week 12 chap 4 8.18 but for a = 1 and f(x) = ln(1+x) but for a = 0 and f(x) = tan(x) out to x**5 week 13 chap 4 9.5, 9.7, 9.10 (rec: 9.6, 9.8, and 9.9) week 14 chap 4 10.4 (rec: 10.5) chap 4 11.5(d), 11.7(b) (rec: 11.5c and 11.7c) ALSO use arcsin(1/2) and the power series expansion of arcsin(x) to compute pi to four decimal places; JUSTIFY THE CORRECTNESS of your answer. (It is OK to use a calculator to evaluate fractions, but, for fun, it may be best to do them via old-fashioned long division. You can then say that you have computed pi by yourself at least once in your life!) -no more HW- ================================================================= MATH 2283 Spring 2008 TEXT: "Sequences, Series, and Foundations" by Wayne Richter LECTURER: Prof. Dennis Hejhal Vincent Hall 220, Phone 625-4557 Email hejhal@math.umn.edu Office Hours _______________________ (or by app't) EXAMINATIONS: There will be 2 one-hour tests and approximately 10 weekly quizzes (10-15 minutes long). The tests and quizzes will be given during the recitations. The sections covered by the tests will be announced in lecture. Quizzes will be similar to homework problems. 2 tests 2 x 100 = 200 pts. HW + quizzes 100 pts. final exam 200 pts. -------------------------------------------- TOTAL points 500 pts. For each student, the two lowest quiz grades will be thrown out. There will be recommended homework (that you should know how to do) and _starred_ homework that should be handed in weekly to the T.A. The starred homework will be given an approximate grade. For the latest list of (starred) homework, see http://www.math.umn.edu/~hejhal (click on 2283). Probable Dates for Hour Exams: Feb 28, Apr 10 or 15. ABSENCE FROM HOUR EXAMS: Missing an hour test is permitted only for the most compelling of reasons. Except in extraordinary situations, you should obtain permission to miss a test in advance. If you are excused from taking an hour test, your score for that test will be determined from your performance on the final exam. WITHDRAWAL: See _Spr Semester 2008 Class Schedules_ for policies concerning cancellations. GENERAL REMARKS: Math 2283 is intended as a "gentle introduction" to the type of mathematical reasoning used in more advanced mathematics courses. The main topics in this course are infinite sequences, infinite series, and Taylor expansions. A sufficient amount of foundational material is developed to permit a reasonable understanding of the theory underlying the aforementioned topics. Most students will find the text challenging in parts. For this reason, I will often try to expedite matters by highlighting the main passages and footnotes. In certain places, I may _deviate_ from the text and use classtime to present a more streamlined approach. Exams will be based on both the material covered in the text _and_ on any supplements presented during lecture. SCHOLASTIC CONDUCT: see www.itdean.umn.edu/students/policies/dishonest.html ** POLICY ON INCOMPLETES: given in exceptional circumstances; requires a contract between student, professor, and dept office; student must have at least C- performance in class prior to an INC being granted. APPROXIMATE SCHEDULE Week Of Sections 1/21 1.3, 1.4 1/28 1.4, sets, logical notation, countability, 2.1 2/4 2.2, 3.1 2/11 3.2 -- 3.4 2/18 3.5, 3.6 2/25 3.6, 3.7 3/3 3.7, 4.1 3/10 4.2, 4.3 3/17 spring break 3/24 4.3 -- 4.5 3/31 4.5, 4.6 4/7 4.7, 4.8 4/14 4.8 4/21 4.9, 4.10 4/28 4.11 5/5 review of earlier material