## Math 300: Introduction to Mathematical Reasoning

Section 02 MTh3 12:00P-1:20 ARC-205 BUS. Section 06 TTh4 1:40P-3:00 LSH-A121

Instructor: Chris Woodward, Hill 336, 5-2466, ctw(you-know-what)math.rutgers.edu.

This course is specifically intended to help Mathematics majors to prepare for 640:311, 640:351 and other proof-oriented courses. It is highly recommended for any mathematics major who is not already experienced in doing mathematical proofs.

Text for Fall 2007: D. Smith, M. Eggen, & R. St. Andre, A Transition To Advanced Mathematics, Brooks/Cole, 2001 (6th ed.)

Grading: Homework 20%, class participation 10%, each midterm 15%, final 40%

Dates of the midterms are Thursday, October 11 and Thursday, November 15. Here is a practice exam for the first midterm. Here is a practice exam for the second midterm. Here is a (somewhat quickly written) practice exam for the final. (In problem (4), it should say "equivalence relation on A union B). Please note that I will not make any changes to the exam grades once the exams have left the classroom, other than mistakes in adding the scores.

The first homework (due the second class) is Problems 1.1 - 1.4, 2.1 from the notes. Unfortunately there is a typo in 1.1 - knight and knaves are switched.

The second homework (due the third class) are the Problems from Smith, Section 1.1 problems 2 (b,e,h,k) 3 (d,f,i) 4 (a,d,g,i,k) 5 (a,b,d) 8 (a,c). Section 1.2 4 (a,b,d,h,i) 5 (a,b,d,k) 6 (a,d) 9 (a,e,f) 10 (b,c) 13 (b,d,f)

The third homework (due the fourth class) is from the course notes, Problem 6.6 (2,8,11), Problem 7.6 (1,4,7,10,13,14), Problem 7.7.

The fourth homework is from the notes, 8.3 (7,9,12,14), 9.3, 9.4 (2,3,6,22,30).

The fifth homework from the book, 1.6: 1 (b,d,h), 2 (a,c), 7 (e,f).

The sixth homework is from the book, 2.1: 1,2,4,5,13.

The seventh homework is form the notes, problems 12.5,12.7,12.9, 12.10, and Problem 1 (f,i). The language "hypothesis-free demonstration" should be taken to mean "proof". Problem 12.13 is extra credit; it really should read "S = { T, T is not in T }".

The eighth homework is from the book, 3.1:1,5,9,12.

The ninth homework is from the notes, 13.1,13.2,13.6,13.7,13.8,13.9.

Section 6 had some homework assigned from the book 4.1: 1(a,d,g,j), 4 and notes 14.1,14.2,14.3,14.4. Section 2 will come back to this later.

The tenth homework is from the notes (third packet) 15.2,15.4(2,3,4),15.5(3).

The eleventh homework is 15.7(2,4,5),15.10(2,4).

The twelfth homework is 16.1,16.3, and 16.4.

The thirteenth homework is 16.6,16.8.16.10.

The fourteenth homework is 19.4. (Exercise means that that step needs more justification, which you are supposed to provide in your paragraph proof.) Please pay attention to style when writing your proof. Have you used complete sentences etc. The fifteenth homework is 9.7 (2) (5). (Examples of paragraph proofs.) Please pay attention to style.

The sixteenth homework is from the fourth hand-out, 14.21, 14.24 and 14.25 (2)(3).

The seventeenth homework is 14.9.(2)(3), 14.11, 14.12.

The eighteenth homework is 14.17, 14.19, and 14.20.

The second midterm will cover from equivalence relations and paragraph proofs, up to and including the fundamental theorem of arithmetic (prime factorizations), induction, and modular arithmetic.

Section 2 had some homework assigned on functions, namely, from the book 4.1: 1(a,d,g,j), 4 and notes 14.1,14.2,14.3,14.4. Section 6 already had this assigned.

The nineteenth homework is from the handout on rationals, 18.5(3) and 18.6-18.9.

The twentieth homework is 19.4, 19.7, 19.8. 19.4 has a typo, the third limit should be 2. Also, please note that the third problem in 19.4 is much harder than the other problems, and requires a lot of work.

The twenty-first homework is from the notes, 19.18, 19.19.

The twenty-second homework is on cardinality, problems 13.24, 13.27, 13.28 (transitivity only), 13.29 (3), 13.30 (5).

The twenty-third and last homework is 20.2 from the notes, and 4.5 #8 and 7.1 #2,3,5(a),6 from the book.

The work you turn in must be your own. You may discuss with other students from the class, as long as you write up your solutions by yourselves, and note whom you have collaborated with on your submitted work.

Tutoring is available for Math 300. Iuliana Radu , Every Monday at 6-7 at ARC 332, and, Every Tue. 7-8 at ARC 332.

Note: For those of you taking the computer science course on discrete structures, there is in fact a lot of overlap. However, there is much more emphasis in this class on writing proofs. The classes are not really equivalent.

The best way to reach me is by e-mail. If you send me an e-mail about a homework problem, please remember to type the problem in the e-mail; I do not always have access to the book or course notes.

The final exam is scheduled for Section 02 Dec 20, 12pm - 3pm, and for Section 06, and for Section 06 Dec 21, 12pm-3pm. The exams are in the same room as the lectures.