Math 8 - A Transition to Higher Mathematics - Spring 2009

Instructor: Alex Dugas my homepage
Office: 6510 South Hall
Office Hours: W 2 - 3, Th 10 - 11, F 11 - 12.

Prerequisites: Math 3B (with a grade of C or better).

Text: A Transition to Advanced Mathematics; 6th edition.  By Smith, Eggen and St. Andre.  Thomson Brooks/Cole 2006.

Lecture: MWF 1:00 - 1:50  in 1420 Phelp.

Section: You must sign up for and attend a discussion section as well.  The section times and locations for this course are as follows: 

• TR   4:00 - 450,  Girv 2129
• TR   5:00 - 5:50, HSSB  1215

The GSI for this course is Ricardo Garza.  His office is 6423T South Hall, and his office hours are:

• M   3:30 - 4:30
• TR  11 - 12
  

Announcements:

• Final Exam Solutions are now available.  The mean was 52/80 and the median was 51/80.
  
• Review Session: Ricardo will hold a review session Saturday 2 - 4 pm in South Hall 6635.
• Office Hours:  I will hold office hours Tuesday (6/9) 1 - 3 pm.
  
• Final Exam:  The Final Exam is Wednesday June 10, 4 - 7 pm.  It will be cumulative, but focus a little more on topics covered since the midterm.  Here is a Sample Exam and Solutions.  It is roughly the same length and difficulty as the actual exam.  Here is an additional Review Sheet which lists important topics and includes more practice problems. Solutions to Review Problems are now ready.
  
• Homework Solutions. Here are Homework 7 Solutions. More Homework Solutions will be posted later this week.
  
• Solutions to Midterm.  Graded exams should be passed back by section on Tuesday.
  
• Homework Solutions. Here are Homework 5 Solutions. Here are Homework 4 Solutions
  
• Midterm 1 is next Wednesday 5/6 in class.  It will cover Chapter 1 and Sections 2.1-2.3 from the text.  Here is a review sheet with practice problems and solutions.  You may also try an old exam and view the solutions.  Be aware that not every topic from the review sheet will be covered on the exam.   The review sheet also features problems on material that will be covered in class this week.  The solutions (when posted) may be helpful for homework 5.

Course Timetable (subject to change)
Date	Topics	Reading	Homework	Due Date
M 3/30	Games		Homework 1	M 4/6
W 4/1	Graph Theory Intro
F 4/3	Propositional Logic: Propositions, Logical Connectives: And, Or, Not Truth Tables.	1.1: p. 1 - 5	Homework 2 1.1: 1) b,d,f,l; 2) d,f; 3)d; 4) l,n; 5, 12 1.2: 1) b,c,h,i; 2) b,c,h,i; 4) b,d,h,i; 6)d; 9) a,c	Mon 4/13
M 4/6	Logical Equivalence.	1.1: p. 5 - 8,
W 4/8	Conditionals.	1.2: p. 11-14
F 4/10	Quantifiers:  Universal (for all), Existential (there exists). Handout	1.3	Homework 3	Mon 4/20
M 4/13	Quantifiers (cont.): Sets, membership.	1.3:
W 4/15	Proofs: Direct and Indirect. Rules of Inference.	1.4: p. 28-35 1.5: p. 39-40
F 4/17	Proofs: Proof by Cases. Proof by Contradiction. Biconditionals.	1.4: p. 35-6 1.5: p. 40, 42-4	Homework 4: 1.4: 7)i,j; 8, 9)a. 1.5: 4)a; 6)a,d;  7)b; 12. 1.6: 4.	Tue 4/28 (in section)
M 4/20	Proof by Contradiction. Prime Factorization.	1.5: p. 40-42
W 4/22	Rational/Irrational numbers. Proofs with Quantifiers.	1.6: p. 47-53
F 4/24	Sets.  Set Equality.  Set-Builder Notation.	2.1: p. 69-73	Homework 5:	Tue 5/5  (in section)
M 4/27	Empty Set.  Subsets.  Set Operations: Union, Intersection, Complement.  Venn Diagrams.	2.2: p. 78-83.
W 4/29	Relation between Sets and Propositions.  Examples of Proofs involving Sets and Set Operations.
F 5/1	Worksheet with Solutions: Sets vs. Propositions.  Indexed Families of Sets.	2.3: p. 86-92
M 5/4	Indexed Families of Sets.  Unions and Intersections.
W 5/6	Midterm 1
F 5/8
M 5/11	Principle of Mathematical Induction (PMI).  1st and 2nd versions.  Proof by contradiction using PMI.	2.4: p. 96-100	Homework 6: 2.4: 5) b, c, d   8) b,c, g, l, m 2.5: 1, 2, 5) a,   12	Tue 5/19  (section)
W 5/13	More examples of PMI	2.4: p. 101-3, 105
F 5/15	Strong / Complete Induction.	2.5: p. 110-14
M 5/18	Cartesian Products.  Relations.	3.1: p. 131-6	Homework 7: 3.1: 4a; 8)b, i, j;   11) a-e; 3.2: 1)i, j; 2)b, c;   4)a, b, c; 8 3.4: 8	Tue 5/26   (section)
W 5/20	Properties of Relations.  Equivalence Relations.  Partial Orders. Congruence Modulo n.	3.2: p. 145-50  3.4: p. 160-61
F 5/22	Equivalence Classes.  Functions as Relations.  Graphs, Composition.	3.1: p. 137-40 4.1: p. 179-83
M 5/25	Memorial Day: No Class!
W 5/27	Inverse Functions. Bijective Functions. One-to-one/Injective, Onto/Surjective	3.1: p. 141-2  (4.1: p. 184-5)  4.2: p. 189-90  4.3: p. 198-203	HW #8 4.1: 1)e,f,i; 3)b,e 4.2: 1)b,f,g; 3)b,f,g; 4.3: 1)b,j,h; 2)b,j,h; 4, 6, 8	Th 6/4
F 5/29	Composition and 1-to-1/Onto. Inverse of a composition.	4.2: p. 190-2  4.3: p. 203-4
M 6/1	Cardinality.  Equipotent Set.  Examples.  Definitions of Finite, Infinite, Countably Infinite, Uncountably Infinite.	5.1: p. 221-4
W 6/3	Countable Sets, Cartesian Products.  Uncountable Sets.	5.2; p. 230-35
F 6/5		5.3: p. 237-40
W 6/10	Final Exam - 4:00 - 7:00 pm

Course Content and Goals:  We will cover most of Chapters 1, 2 and 4 in the text and additional topics from Chapters 3 and 5 as time permits.  Initially, the focus will be on understanding new notation and writing proofs involving easy math, but we will gradually move to more abstract concepts and problem solving strategies.  By the end of this course you should be able to 

• Understand and use mathematical notation relating to sets, functions and quantifiers.
• Write clear, organized and logically correct proofs.
• Think abstractly about fundamental mathematical concepts, including sets and functions.
• Approach problems that you don't know how to answer, and devise strategies to solve them or come up with proofs on your own.
  

Individual Meetings.  You must meet with me at least twice during the quarter.  These meetings are informal, but mandatory.  They are meant to give me a chance to get to know each of you and your interests, and so that you can give me feedback about the class and keep track of your performance.  The first meeting should be during the first three weeks of the class: drop by my office hours, talk to me after class, or email to schedule an appointment.  The second meeting should be sometime after the midterm.

Section/Classwork:  Attendance and participation in a discussion section is mandatory for this course.  In section, your T.A. will answer questions, review the homework, and cover additional examples.  But, more importantly, you will work on problems, often in small groups.  Your  work will occasionally be graded and contribute to your grade for the course.

Homework:  Homework exercises will be assigned in lecture and listed on the course webpage.  Homework will be turned in once a week in lecture, usually on Fridays.  You may work together on homework problems; however, you must write up your answers individually.  You must show all your work in order to receive full credit.  Late homeworks will not be accepted.  However, your lowest homework score will be automatically dropped. 

Exams:  There will be an in-class midterm exam on Wednesday May 6, 1:00--1:50 pm.  Please arrive promptly.  The final exam will be Wednesday June 10, 4:00--7:00 pm.  The problems on the exams will be similar to those seen in class or on the homeworks.   No make-up exams will be given, except in extraordinary circumstances.  If you have a serious conflict with any of these exams or miss one for any reason, it is your responsibility to notify me immediately so that other arrangements may be made.

Grades: Grades will be computed from your scores on homeworks and exams as follows:  Classwork/Section/Participation = 15%, Homework = 30%, Midterm = 20%, Final = 35%.  No letter grades will be assigned until the end of the semester, and the exact grading scale will be curved relative to the difficulty of the exams.  However,  a 90% or above will guarantee you at least an A, an 80% will be at least a B, and 70% will be at least a C.