Introduction to Mathematical Proof (Fall 1998)

Additional TA information

The schedule for the sections is as follows: M 8-9:10am Merril Acad 003, and TH 4-5:10pm Cowell Acad 216.

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Course description

Introduction to various tools and techniques for proving mathematical theorems.

Course prerequisites

Basic knowledge of Calculus as taught in Courses 11 A-B, or 19 A-B; or permission from the instructor.

Required textbooks

Foundations of Higher Mathematics, by P. Fletcher & C. Patty, third edition.

Lecture and reading schedule

Week #1 (Oct 5-9): 1.1, 1.2, 1.3, 1.4, 1.5, 1.6.

Week #2 (Oct 12-16): 2.1, 2.2, 2.3, 2.4, 3.1, 3.2.

Week #3 (Oct 19-23): 3.1, 3.2, 4.1, 4.2.

Week #4 (Oct 26-30): 4.2, 4.3, 4.4, 4.5.

Week #5 (Nov 2-6): 4.5, 4.6, 4.7, 5.1.

Week #6 (Nov 9-13): 5.1, 5.2, 5.3, 5.4.

Week #7 (Nov 16-20): 5.5, 6.4, 7.1.

Week #8 (Nov 23-27): 7.1, 7.4, 7.5.

Week #9 (Nov 30-Dec 4): 7.5, 8.1, 8.2.

Week #10 (Dec 7-11): 8.3, 8.4, 8.5.

Assignments

There will be weekly homework assigments to be turned in class each Friday (Late HW's will not be accepted). Homework problems will be announced in class at least a week prior to their due date. These assignments will also be posted on the web site: "http://wwwcatsic.ucsc.edu/~syllabus/math-100" where a copy of this syllabus is posted and will be updated periodically. For this and other course related information you may also check the instructors web site at "http://www2.ucsc.edu/people/ghomi/".

HW#1 (Due Oct 9) 1.1) 2 a e, 6, 7, 9, 11; 1.2) 15 a b, 17, 23 a b, 25 b, 39.

HW#2 (Due Oct 16) 1.3) 41 a b, 42, 44, 46, 54; 1.4) 56, 57, 61, 63, 66, 72, 74; 1.5)82, 85, 90.

HW#3 (Due Oct 23) 2.1) 4, 7, 9, 10, 11, 13, 16, 20; 2.2) 23, 26, 30, 31, 34, 39, 50; 2.3) 55, 71; 2.4)73, 76, 79.

HW#4 (Due Oct 30) 3.1) 1 a h, 2, 3, 6, 7, 8, 9, 12, 13; 3.2) 20, 24, 31, 35, 36; 4.1) 1, 2, 3, 6, 9, 13; 4.2) 17, 18, 19.

HW#5 (Due Nov 6) 4.3) 26, 28, 30, 34, 35, 40, 45; 4.4) 48, 49, 50, 52, 53, 58. 4.5) 62, 63.

HW#6 (Due Nov 13) 4.5) 64, 65, 73, 76; 5.1) 1, 4, 6, 7, 12.

HW#7 (Due Nov 20) 5.2) 18, 20, 21, 23, 28; 5.3) 31, 32, 33, 34, 37; 5.4) 39, 40, 42, 44.

HW#8 (Due Nov 30) 5.5) 46, 47, 56; 6.4) 59, 60, 61, 63, 65,
67, 71, 73; 7.1)4, 5, 6, 7, 8, 11, 12.

HW#9 (Due Dec 4) 7.4)24, 25, 26, 28, 32; 7.5)38, 39, 40, 43.

HW#10 (Due Dec 11) 8.1)2, 3, 4, 5, 6, 7, 11; 8.2)13 a b, 14, 15, 19; 8.3)22, 23, 24, 25, 28, 29, 30, 31.

Tests and exams

There will be at least one midterm, plus a final exam. One of these exams, or perhaps all of them, might be take home exams.

Grading

The final grade will depend on homeworks (about 30%), midterms (about 30%), and the final exam (about 40%). Other factors such as class participation may also affect the final grade.