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
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.
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.