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MATHEMATICS 3345: Foundations of Higher Mathematics
AU 2019, MWF 11:30AM-12:25 PM in Journalism Bldg 304
Instructor:
Dr. Rodica D. Costin
Office: 436 Math Tower
Office hours: M F after class (12:30-1:30) or by appointment, or by appointment
e-mail: costin"dot"10

Homework assignments and other information are posted below after each class.
What is logic good for?

The following problems are due on Wed Aug 28, at the beginning of class.

Wed Aug 21 Let A and B be propositions. Prove that the disjunctions AVB and BVA are logically equivalent in two ways:
a) by using a truth table
b)using words.
What is a sentence?

Fri Aug 23 Solve Exercise 1 on p. 5.
Mon Aug 26 Solve Exercise 2 on p. 7.

The following problems are due on Wed Sept 4.

Wed Aug 28
Solve 8 and 9 (on p.11). Read the paragraph before problem 9.
Fri Aug 30
Solve 24 on p. 20.

Solve (in preparation for the midterm), but do not submit:

Wed Sept 4 Solve Example 3.3 on p.27 and check your solution against the one in the textbook. Do not submit for grading!
Fri Sept 6 Review guide
Mon Sept 9 Midterm test 1.

The following problems are due online, on Carmen, on Sept. 18.

Wed Sept 11 Prove Theorem 3.10 (on p.32) following the model of the proof of Theorem 3.8.
Fri Sept 13 Exercise 10 cdef, 11 Correction: a,b. (in Sec. 3, on p. 35).
And Ex. 14
efgh on p. 37
Mon Sept 16 Exercises 1 and 2 p.41 (section 4)

The following problems are due online, on Carmen, on Sept. 25.

Wed Sept 18 Exercises: 5 (on p.42), 8acd (p.43) on p.43, 10adf on p.44.
Exercises 8 and 10 are very important, you should know how to solve all the points there.

Fri Sept 20:  Exercises: 13 and 14 on p.46.

Read General Guidelines for Constructing Proofs on p.55-57 and recognize using them in your proofs.
Mon Sept 23:  Exercises 1 and 2 (on p. 60, in Section 5).

The following problems are due online, on Carmen, on Oct 2nd.
Wed Sept 25 Exercise 4 on page 61.

Use the exercise above to deduce a factorization formula for a^n-b^n.
Solve Exercise 5 in two ways: (i) by using the factorization formula for
a^n-b^n; (ii) by induction.
Fri
Sept 27  Exercise 11 on page 65, and Exercises 12, 13a on p.66
Mon Sept 30  Use complete induction to show that any natural number n greater or equal than 5 can be written as n=2k+3j for some non-negative integers k,j.
The following problems are due online, on Carmen, on Oct 9th.
Wed
Oct 2  Prove the following generalization of the Theorem on Division by a Prime:

Let p be a prime number and x1,x2,...,xn be integers (n>1). If p divides the product  x1 x2...xn then there is some k in {1,2,...,n} so that p divides xk.
Fri
Oct 4 Exercise 4  on page 86.
Bonus! 5 on page 86.
Mon
Oct 7  Section 10! Exercise 1 on p 104 and 4bc on p 106

The following problems are due online, on Carmen, on Oct 23.
Wed
Oct 9  Solve these problems now, in preparation for the midterm: in Section 10, Exercises 5 p.106, 8 on p 108, 11, 12 Solve, but do not submit, the exercises on the review sheet.

Mon Oct 14 Review guide
Wed Oct 16 Midterm II
Fri Oct 18  Let A, B be sets. Prove that A-(A-B)=(A intersect B) using complements
Exercise 18 ae, Exercise 19a (on page 110)

Mon Oct 21  Exercise 18 b, Exercise 19c (on page 110), Exercise 22b (p 114). Do not forget to submit the problems assigned on Oct. 9th too!

The following problems are due online, on Carmen, on Oct 30th
Wed. Oct 23 Exercises 24, 25, 26. Do for practice 27, but do not submit for grading.