Michael J. Grant Campus
MATHEMATICS DEPARTMENT
Fall 2009 Syllabus — A Survey of Mathematical
Reasoning
INSTRUCTOR
INFORMATION
Name: Alexander
Kasiukov
Office: Academic
wing of the
Phone: (631) 851-6484
Email: kasiuka@sunysuffolk.edu
Web Page: http://www2.sunysuffolk.edu/kasiuka/
Office Hours: See
schedule. Additional tutoring is available in the Center
for Academic Excellence, Room MA 129
COURSE INFORMATION
Name of Course: A Survey of Mathematical Reasoning
Catalog Number: MAT 101 (MA 21)
CRN: 93445
Number of Credits: 3
Number of Contact Hours: 3
Prerequisite: Successful Completion of MAT 007 (MA 07), Algebra I
Grading: Graded on an A-B-C-D-F-W basis.
Meets: Monday, Wednesday: 2:00—3:15, Room MA 114
Final Exam: Monday, December 14, 2009
Textbook: Alfred Tarski, Introduction to Logic
Course Philosophy:
Liberal arts mathematics course which provides insight into nature of mathematical reasoning by examining basic structures such as logic, sets, real numbers, numeration systems and inductive reasoning
Topic Outline:
I. Core Topics:
1. Logic (Math thinking) (3—5 weeks)
(1). Deductive thought
(2). Inductive thought
(3). Conjecture, proof
(4). History of logic
(5). Definitions:
A). Truth tables
B). Arguments, theorems, proof (direct and indirect)
C). Validity
2. Sets (2—3 weeks)
(1). History
(2). Definition
(3). Operations with sets
(4). Venn diagrams, survey problems
(5). Arguments, theorems, proof, conjecture (optional)
(6). Cardinal numbers (optional)
(7). Infinite sets (optional)
(8). Finite sets
(9). Equivalent sets
(10). 1—1 correspondence
(11). Cantor's theorems (optional)
II. Additional Topics (at least three, 2—3 weeks each):
1. Real numbers
(1). Natural numbers
(2). Integers
(3). Rational numbers
(4). Irrational numbers
(5). Properties of the systems (closure, etc.)
(6). Calculators
A). History
B). Algorithms
C). Order of operations
2. Switching Circuits
(1). Definitions
(2). Problems
(3). Theorems
3. Boolean algebra
(1). Definitions
(2). Theorems
(3). Proofs
4. Numeration system
(1). Historical
(2). Positional
5. Number Bases
(1). Unique representation
(2). Other than 10 bases
(3). Connecting to other bases
(4). Application to computer
6. Inductive Reasoning
(1). Find the n-th term of a sequence
(2). Prove sum of arithmetic and geometric series
7. Computers
(1). History
(2). Processing
(3). Flow chart
(4). Programming
Learning Objectives
Upon successful completion of this course, students should be able to:
1. Distinguish between deductive and inductive reasoning and be able to apply each in problem solving;
2. Make connections between mathematical discoveries and the history of human thought;
3. Perform the basic operations of set theory including: intersection, union and complement;
4. Analyze basic data-type questions (survey results) using subsets and Venn diagrams;
5. Translate verbal statements into symbolic forms of implication, conjunction, disjunction and biconditional;
6. Test for the validity of arguments using various methods, indirect as well as direct;
7. Define logical connectives using truth tables and be able to discover tautologies and prove theorems using truth tables;
8. Convert to any base using expanded numeral concept as well as the division algorithm.
9. Distinguish between rational and irrational numbers using the infinite decimal concept;
10. Solve problems on a calculator or computer involving loans, interest, mortgages, annuities and life insurance;
11. Analyze switching circuits using logical equivalences;
12. Write programs in basic which utilize a loop, using proper structured programming techniques;
13. Diagram the logical design of a computer or calculator.
POLICIES
AND PROCEDURES
Procedures
for accomplishing the Course Objectives:
· Individual work of a student
· Participation in problem solving in class
· Preparation of the assigned homework and reading
· Instructor's office hours.
·
Utilization of
free tutoring and supplementary materials available in the
Student Requirements for completion of the course:
Students must attend class, do homework assignment, take all the quizzes and the comprehensive final exam.
Grading:
There will be approximately 15—20 quizzes, given regularly (at least once a week) in class. They will last no more than 20 minutes each and will cover current material. There will be a final exam at the end of the course. It will cover all the material of the course. If a test (i.e. a quiz or the final exam) is missed, then the grade 0 is assigned for that test.
Final score of a student =
sum of all quiz scores (out of 75 possible)
+
the final exam score (out of 25 possible).
Letter grade of a student =
A, if the final score is 90 and above;
B+, if the final score is 85—89;
B, if the final score is 80—84;
C+, if the final score is 75—79;
C, if the final score is 70—74;
D+, if the final score is 65—69;
D, if the final score is 60—64;
F, if the final score is below 60;
W, if the student withdraws officially, by returning a withdrawal slip with my signature to the Registrar's Office before mid-semester (as defined by the academic calendar).
Attendance:
All students are expected to attend every session of each course for which they are registered. Students are responsible for all that transpires in class whether or not they are in attendance. The College defines excessive absence or lateness as more than the equivalent of one week of class meetings during the semester. Excess absence or lateness may lead to failure in a course or removal from the class roster.
Make-ups:
Make-up tests will be given only for documented emergencies, and then only at my discretion and convenience. However, if you have a good reason, please do ask for consideration.
Disruptions:
Disruptive behaviors, as defined by the Student Handbook, will not be tolerated. College policy allows for the removal of disruptive students from class for the remainder of a class session in progress. Repeated disruptions in the classroom will lead to disciplinary action as specified in the Student Handbook. Pagers and cell phones are to be turned off at all times. If anyone wishes to reach you in an emergency, he or she should call the Mathematics Department Secretary (see the phone number above).
Use of Calculators:
Use of calculators is
not allowed — in the class and during the final exam;
not recommended — during home work.
Students with special needs:
If you are a student who has a
disability and need reasonable accommodations, then please give me an advance
notice about your special needs. If you have specific questions about obtaining
these accommodations, you can call the