**MATHEMATICS
3345: Foundations of Higher Mathematics**

**AU 2019**, MWF
11:30AM-12:25 PM in Journalism Bldg 304**
Instructor:** Dr.
Rodica D. Costin

Syllabus and
General Information

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.

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

Fri Aug 30 Solve 24 on p. 20.

Wed Sept 4 Solve Example 3.3 on p.27 and check your solution against the one in the textbook. Do

Fri Sept 6 Review guide

Mon Sept 9 Midterm test 1.

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)

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).

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.

Wed

Wed

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.