Math 8 - Transitions to Higher Mathematics - Winter 2007

Instructor: Alex Dugas my homepage
Office: 6510 South Hall
Office Hours: M 1-2, Th 1-3

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

Text: Larry Gerstein.  Introduction to Mathematical Structures and Proofs.  Springer-Verlag 1996.

Lecture: T Th 11:00 - 12:15  in 1217 BSIF.

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


The GSI for this course is Chad Wiley.  His office hours, in SH 6431N, are:


Announcements:

 

 

 

Course Timetable (subject to change)

    Date    

    Topics    

    Reading    

    Homework  

    Due Date    

Tu 1/9

Propositions.  Logical Connectives:
Not, And, Or.  Truth Tables.

Ch. 1.1-1.2

Ch. 1.3: Ex. 1, 2, 3, 4, 6, 8, 18

 

 1/17

Th 1/11

More Truth Tables.  Conditional Statements and Implications.

Ch. 1.3

Tu 1/16

Biconditionals.  Converse and Contrapositive of Implications.
Direct and Indirect Proofs.


Ch. 1.4



Ch. 1.4: Ex. 2, 4, 5
Ch. 1.5: Ex. 3, 4

 


 1/22

Th 1/18

Logical Equivalence

Ch. 1.5

Tu 1/23

Functional Propositions.  Sets.  Russell's Paradox.  Axiom of Separation

Ch.  2.1-2.2

Ch. 2.1: Ex. 2, 3b,d, 5, 7

Ch. 2.3:  Ex. 1, 2, 7, 9 (give brief explanations for 9)
Class Work: Ex. 1-8


 1/29

 

Th 1/25

Universal and Existential Quantifiers

 

Ch. 2.3

Tu 1/30

Set Inclusion and Subsets.  Unions, Intersections, Complements, Set Difference.  Venn Diagrams.

Ch. 2.4-2.5

Ch. 2.4:  Ex. 1, 7, 9
Ch. 2.5:  Ex. 4, 5c,d, 6,  7

 

  2/5

Th 2/1

Power Sets.  Indexed Sets.

Ch. 2.6-2.7

Ch. 2.6:  Ex. 2a,d, 3, 5
Ch. 2.7:  Ex. 8

Tu 2/6

Cartesian Products.

Ch. 2.8

Ch. 2.8:  Ex. 2, 3, 4, 5


 2/12

Th 2/8

Midterm Exam

Ch. 1.1 - 1.5,
  2.1 - 2.8

 

Tu 2/13

Relations.  Equivalence Relations.  Partitions.   Partial Orders.

Ch.  2.9

Ch. 2.9:  Ex. 4, 6, 10, 20


 2/21

Th 2/15

Congruence Modulo n.  Partial Orders.

Induction.

Ch. 2.10

Ch. 2.10:  Ex. 3, 4, 6, 7, 9

Tu 2/20

Strong Induction.  Binomial Coefficients

Ch. 2.10

 


 2/26

 

Th 2/22

Binomial Coefficients.  Pascal's Triangle.  Binomial Theorem.

Ch. 5.8

Ch. 5.8:  Ex. 2, 5, 7, 9, 10

Tu 2/27

Functions.  Domain, Image/Range, Surjections.  Sets of Functions.

Ch. 3.1

Ch. 3.1:  Ex. 1, 6a,b,c,g, 11a,b,e,f

 
 3/5

 

Th 3/1

Injections. Bijections.
 

Ch. 3.2

Ch. 3.2:  Ex. 2, 4, 6, 9

Tu 3/6

Composition of Functions.  Inverse Functions.

Ch. 3.3

Ch. 3.3:  Ex. 2, 3, 4, 7, 8, 9


 3/12

Th 3/8

Cardinality.  Counting Principles.

Ch. 4.1

Ch. 4.1:  Ex. 3, 4, 5

Tu 3/13

 

Ch.

 

 

Th 3/15

 

Ch.

 

Th 3/22

Final Exam - 12:00 - 3:00 pm

 

 

 

 


Course Content:
The aim of this course is to familiarize students with some of the fundamental tools of mathematics, including sets, functions and proof, and how they are written.  We will cover most of Chapters 1-3 and parts of Chapters 4 and 6 in the text.

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 in the table above.  All homework problems assigned in a given week are due on the following Monday in section (or Wednesday, if Monday is a holiday).  You may work together on homework problems; however, you must write up your answers individually.  You must show all your work in order to recieve full credit.  Late homeworks will not be accepted.  However, your lowest homework score will be automatically dropped.

Exams: There will be one in-class midterm exam on Thursday February 8, 11:00 - 12:15.  Please arrive promptly.  The final exam will be Thursday March 22, 12:00 - 3:00 pm.  The problems on the exams will be similar to ones from classwork and homeworks.   No make-up exams will be given, except in extaordinary 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 classwork, homeworks and exams as follows: Classwork/Section = 10%, Homework = 25%, Midterm = 25%, Final = 40%.  No letter grades will be assigned until the end of the semester, and the exact grading scale will depend on 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.