MATHEMATICS 3345: Foundations of Higher Mathematics
SP 2019, MWF 9:10-10:05 AM in Bolz Hall 314
Instructor: Dr. Rodica D. Costin
Office: 436 Math Tower
Office hours: Updated M 10:15-11AM and 12:00-12:30 PM,  F  10:15-11AM, 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?

Good reasons to study logic.

The following problems are due on Wed Jan 16, at the beginning of class.

 Monday Jan. 7 Solve Exercise 1 on p. 5.
Typo on the General info hand-out: midterm 2 on March 4th (as seen below).
What is a sentence?

Wed Jan. 9 Solve Exercise 2 on p. 7.

Fri Jan. 11 Solve Exercises 6, 7, 8, 9 and read the paragraph above it, 10, 11, 15 (like in class, do not make discharging arguments, but say when you use conditional proof and modus ponens).
 Optional (do not submit for grading): Since it is interesting: 5 and read Remark 2.7. CS majors, you need this: 10 and pay attention to the paragraph above it.

 See here instructions for writing up your homework assignments.

Monday Jan. 14  Solve problem 17, 19, 20, 23. New office hours, see above.
 
The following problems are due on Wed Jan 23, at the beginning of class.
Wed Jan. 16  Solve Exercise 1 abefi on p.29, but do not submit. Do this asap. If you have trouble with these seek help (come to office hours, seek peer help, etc.)
                      Solve and submit: Exercise 1 all the other points (cdghjk). I may add more exercises today after class.

Fri Jan. 18  Solve exercises 2 (p.29), 4, 5, 7

Monday Jan. 21: MLK Day - No Classes
 
The following problems are due on Wed Jan 30, at the beginning of class.
Wed Jan. 23 Solve exercises 10ef (p.35), 14(p.37). Solve them this week, in preparation for the midterm!
 
Fri Jan. 25 Section 4, Exercises 1, 2, 3. Solve them this week, in preparation for the midterm! Review guide.

Monday Jan. 28  Midterm 1

The following problems are due on Wed Feb. 6, at the beginning of class.
Wed Jan. 30   Brr  day

Fri Feb 1st Solve exercises 5 (p.42), 6, 7, 8 (I deleted 13 here and posted it down)

Mon Feb 4 Solve exercises 10a,b,d,f,g (p.44), 11, 13

The following problems are due on Wed Feb. 13, at the beginning of class.
 Wed Feb 6 Solve exercises 14 (p.46, Section 4), and from Section 5 (p.60): 1, 2,3a, 4

Fri Feb 8 Solve exercises 5, 6, 11, 18.

Mon Feb 11 Solve exercises 19, 20 (p.71).

The following problems are due on Wed Feb. 20, at the beginning of class.
Wed Feb 13 Solve exercises 22 (p.71), 12 on page 45, and exercise 4 on p.86.

Fri Feb 15 Solve exercise 5 (p. 106). Solve by Monday, but do not submit for grading, exercises 1,2,4 in Section 10.

Mon Feb 18 Solve exercises 8, 9 (yes, we covered in class the material needed for these)
The following problems are due on Wed Feb. 27, at the beginning of class. 
Wed Feb 20 Solve exercises 10, 11, 18

Fri Feb 22  Solve exercises 19, 20, 22

Mon Feb 25 Solve exercise 25.

The following problems are due on Wed March 6, at the beginning of class.
 Wed Feb 27 Solve exercise 26 and the following variation of ex. 5 p106:

Exercise 5': Let S be a set such that for each nonempty set A, S is included in A. Show that S is the empty set.
 
Fri March  1st Review guide and exercises

Mon March 4   Midterm 2


The following problems are due on Wed March 27 (not the Wed after the Spring Break). But solve them as we go.
Wed March 6 Solve exercise 33 abcd. Also, prove what we claimed in class, that [1,4]xR intersected with Rx[2,3] equals [1,4]x[2,3].

Fri March 8

Have a great Spring Break!

Mon March 18   Exercise 4 on page 123

Wed March 20 Exercise 15 on page 127

Fri March 22 Exercise 20a on page 129
                      Correction to the last problem we did in class, with g(x)=x^2-2x. As we noted, Rgn g=[-1, oo) so g1:[1,oo)-->[-1, oo) and g2:(-oo, 1]-->[-1, oo)

Mon March 25 Exercise 26 on page 130

The following problems are due on Wed April 3rd
Wed March 27 Exercise 25 on page 130
 
 Fri March 29 Exercise 15, 17 on page 138



Mon April 1st   Exercise 23 on page 141. The rest of this section is omitted.

The following problems are due on Wed April 10
 Wed April 3 Exercises 8 and 11 on p 182.

Fri April 5 Exercises 13 and 14 on p 183.

Mon April 8 A. Consider the relation on Z given by xRy iff 4 | x^2-y^2. We showed this is an equivalence relation. Find all the classes in Z/R.
                     B. Consider the relation on the set of real numbers given by xRy iff xy>0. Is it an equivalence relation?

The following problems are due on Wed April 17
 Wed April 10

Fri April 12 Exercise 23 on p 187. We stopped sec. 17 there. We have started Sec. 13, so also do Exercise 3 on p 145.

Mon April 15   Exercise 6 on p 146 and 8 on p 148. I have posted review problems below.

The following problems are to help you practice, do not submit them for grading.
 Wed April 17 Exercise 9. (I posted the .pdf file for review.)
                       1. Show that f:A->B is injective iff it has a left inverse (there exists g:B->A such that gof=Id).
                       2. Show that h:A->B is surjective iff it has a right inverse (there exists k:B->A such that hok=Id)
Note that in 1. g is the right inverse of f and f is the left inverse of g. (similarly in 2.)
                       3. Let A,B be finite sets. Prove that  |A union B|=|A|+|B|-|A intersect B|
Show that f:A->B is injective iff it has a left inverse (there exists g:B->A such that gof=Id)                       
Show that f:A->B is injective iff it has a left inverse (there exists g:B->A such that gof=Id)Show that f:A->B is injective iff it has a left inverse (there exists g:B->A such that gof=Id)Show that f:A->B is injective iff it has a left inverse (there exists g:B->A such that gof=Id) Fri April 19 Review problems for the final exam.

Mon April 22   Review. Special additional office hour Thursday Apr 25, 2-3PM
Final exam scheduled for Friday Apr 26. 10:00-11:45am, see Registrar Final Examination Schedule