MATH 8, A TRANSITION TO HIGHER MATHEMATICS.  Winter 2007.


    Class Time: MWF 10:00-10:50 in Arts 1251

    Instructor: Azer Akhmedov                                   Teaching Assistant:  Melissa Flora
    Office: 6702 South Hall                                            Office: South Hall 6431J
    Office Hours: Tue 1:30-3:30, Wed 3-4.                   Office Hours: Mon 3-4, Tue 12:30-1:30, Wed 11-12
    Phone: 893 2889                                                       E-mail:  msflora AT math.ucsb.edu
    E-mail: akhmedovATmath.ucsb.edu                    


    Discussion Sections:  T R  5:00-5:50   HSSB  2251
                                        T R  6:00-6:50   HSSB 1224


    Textbook:  Introduction to Mathematical Structures and Proofs,  by Larry Gerstein.


   

      Midterm1:  Feb 05, in class.      Midterm 2:  Mar 07, in class.
 
      FINAL:  Tuesday, March 20th, 8am-11am. In class.

      Books and calculators are not allowed in the exams. You may use one 3x5 (4x6 in the final) notecard.
      Please bring ID and ONE BIG BLUEBOOK to the final exam.

      MIDTERM 1 covers sections 1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.2, 2.3.
    
      MIDTERM 2 covers sections 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 3.1, 3.2, 3.3.

      SAMPLE PROBLEMS   These are just sample problems for practice.

      Review Session: Monday 10am -11:30am, South Hall 6635.

      MORE SAMPLE PROBLEMS
   

   
   
   GRADING POLICY:  Homework 20%, Quiz 10%, Midterms 40%, Final 30%.

  
   Homework:  Homeworks are due every Friday in class.  Please write neatly and staple your work. I'll drop the lowest score and substitute it with the highest one.

   Course Content: Chapters 1-4. Few sections from Chapter 5. 
   
 
   Quiz:   A quiz will be offered every week in sections. The quizzes are testing the basic understanding of the course.  


     
 
  
  
Date
    Section
                       Topic                
   Homework                  
1/08
  1.1.
  Statements and Propositions
1/10
  1.2.
  Logical Connectives,Truth Tables
1/12
  1.3.
  Conditional Statements
  HWK#1: 
Sec.1.1. # 1, 2.
Sec.1.3. # 1, 2, 3, 5, 6.
1/15
  
  HAPPY HOLIDAY!!!
1/17
  1.4.
  Proofs: Structures and Strategies
1/19
  1.5.
  Logical Equivalences
  HWK#2:
Sec.1.3. # 8, 9b, 11.
Sec.1.4. # 1, 2, 5.
1/22
  2.1.
  Sets
1/24
  2.2.
  Russels's Paradox.
1/26
  2.3.
  Quantifiers.
  HWK#3:
Sec.1.5. # 3, 4, 7.
Sec.2.1. # 2, 3, 4.
1/29
  2.3.
  Quantifiers.
1/31
  2.4.
  Set Inclusion.
2/02
  2.5
  Union, Intersection, Compliment.
 HWK#4:
Sec.2.1. # 5, 6, 7.
Sec.2.3. # 2, 6, 9.
2/05
            MIDTERM 1
2/07
  2.6-2.7.
  Indexed Sets, Power Set.
2/09
  2.8.
  Ordered Pairs & Cartesian Products
 HWK#5:
Sec.2.4. # 1, 4, 6, 8, 9.
Sec 2.5. # 1, 7c, 9. 
2/12
  2.9.
  Partitions and Relations.
2/14
  2.9.
  Equivalence Relation.
2/16
  2.10.
  Mathematical Induction.
 HWK#6:
Sec. 2.6. # 1, 2, 3, 5.
Sec. 2.7. # 1, 2, 5.
2/19
  
  HAPPY HOLIDAY!!!
2/21
  3.1-3.2.
  Surjection, Injection, Bijection.
2/23
  3.3.
  Compositions of Functions.
 HWK#7:
Sec.2.8. # 3, 5.
Sec.2.9. # 2, 3, 6, 15, 20.
Sec.2.10. # 1, 2, 4.
2/26
  3.3.
  Compositions of Functions.
2/28
  4.1.
  Cardinality. 
3/2
  4.2-4.3
  Countable, Uncountable Sets.
 HWK#8:
Sec2.10. # 6, 7.
Sec.3.1. # 1, 3, 5, 11.
Sec.3.2. # 2, 4, 9.
3/5
  4.2-4.3.
  Cantor's Theorem I.
3/7
          MIDTERM 2
3/9
  4.2-4.3.
  Shroder-Bernstein Theorem.
 
 HWK #9:
Sec3.3.  # 6, 7, 9, 11
Sec4.1. # 3, 4, 5, 6.
3/12
  4.2-4.3.
  Cantor's Theorem II
3/14
  4.4.
  More on Infinity.
3/16
  
  Review of Chapter 4.
 HWK#10:
Sec4.2. # 2, 4a, 5, 6, 7.
Sec4.3 #1, 4, 5, 9, 11, 14