MATH 1025

SYLLABUS – MA 1025 – Introduction to Mathematical Reasoning, Summer 2014
Dr. Pante Stanica

LECTURE: T, Th 13:00-14:50pm, Spanagel 208

INSTRUCTOR: Dr. Pante STANICA, 242B Spanagel, 656-2714,
                   pstanica@nps.edu (the most reliable and preferred means of communication);
                   http://faculty.nps.edu/pstanica/index.htm

OFFICE HOURS: T, Th   10:00-11:00am (check with me; I should be in the office before class, as I teach from 8-9:50, as well).
(Be aware that office hours are not a substitute for regular class time)

TEXTS: Discrete Mathematics: An Introduction to Mathematical Reasoning (1st ed.) by Susanna S. Epp;

CALCULATOR POLICY: Only a basic calculator is allowed (but not required).

MATERIAL TO BE COVERED (and Objectives for the course—subject to be adjusted along the way):

HOURS	TOPIC	SECTION
1-1	Mathematical Language: Variables, Sets, Relations	1.1—1.3
2-3	Propositions, Connectives, Equivalence	2.1
2-5	Conditional Statements, Valid Arguments	2.2, 2.3
2-7	Predicates and Quantifiers	3.2
1-8	Nested Quantifiers	3.3
1-9	Inference Rules and Deduction	3.4
2-11	Proofs in Mathematics: Direct Proof of Conditionals	4.1—4.3
1-12	Proofs in Mathematics: Proof by Cases	4.4
2-14	Indirect Proof – Contraposition and Contradiction	4.5, 4.6
1-15	Sequences and Summation	5.1
3-18	Mathematical Induction	5.2, 5.3
1-19	Naive Set Theory (Introduction, element-chasing)	6.1
1-20	Properties of Sets	6.2
1-21	Disproof, Algebraic Proof	6.3
1-22	Functions on General Sets	7.1
2-24	Surjections, Injections, Bijections	7.2
1-25	Composition of Functions	7.3
1-26	Cardinality and Countability	7.4
1-27	Relations (Introduction)	8.1
2-29	Properties of Relations	8.2
1-30	Equivalence Relations	8.3
1-31	Elementary Counting (Introduction)	9.1
2-33	Multiplication and Addition Rules	9.2-9.3
1-34	The Pigeonhole Principle	9.4
2-36	Counting: Combinations , Permutations w/Repetition	9.5
2-38	Combinatorial Reasoning, the Binomial Theorem	9.6
4-42	Exams, Reviews, and Holidays

HOMEWORK: You are encouraged to do as many problems as you can from the book. However the standard (default) assignment for each week is to read carefully the indicated sections and to prepare for homework the problems I will assign in class. The homework will not be collected. However the exams may contain problems from the assigned homework.

TESTS: Two regular class-time tests will be given in Week 4 and Week 8 (may change, but I will announce it in class, about one week in advance), and a final comprehensive take-home exam. The tests will contain approx. 5-10 problems/questions and the final exam will contain approx. 10-20 prob/que (each of the prob/que will be worth 5-10 points for a total of 50 for the tests, respectively, 100 for the final). No make-up tests will be given except in extraordinary circumstances (e.g. illness - present verified doctor's excuse). I reserve the right to give pop quizzes (1-5pts), which will be used toward the final grade, as an add-on (extra credit) to the final score. If the test dates will be changed I will announce it in class at least one week in advance. It is your responsibility to stay informed of such changes. Also, students are expected to read ahead, in order to prepare properly for class.

GRADING: The number of possible points is 200(50test1+50test2+100final). For the letter grade I will use the following scale (be advised that class participation will be considered, especially in the borderline grades) (there are no exceptions from this scale!!!!):
185-200: A 175-185: A- 170-174: B+ 160-169: B 150-159: B-
140-149: C+ 130-139: C 125-129: C- 120-124: D+ 100-119: D
000-099: failing grade.
An unresolved absence from either of the two tests or the final examination will result in a final grade of “FA”.

ACADEMIC HONESTY: Cheating in this course will not be tolerated and will be dealt with as harshly as the University permits. I will report any student behavior that appears contrary to the standards of discipline and academic honesty or violations of the provisions described in the current edition of NPS Student's Catalog.

CLASS ATTENDANCE AND ENVIRONMENT: You should do every attempt to arrive on time and attend each class. You are responsible for the material covered in missed classes. I do not tolerate any rude behavior; however I encourage constructive comments on the material and/or lecture. We have to maintain a class environment conducive to learning therefore I am against bringing “active” cell phones, pagers, and other similar disruptive devices into the classroom. Children may not be brought into the classroom except in emergency circumstances and with my permission. Do not bring food in classroom. When on breaks, please respect other classes in sessions and avoid disturbing them.

NOTES:
* MA1025, Introduction to Mathematical Reasoning is an introductory course in logic and elementary mathematics, to be taken by students of various majors in their refresher quarter. Considerable emphasis is placed on propositional and predicate logic, and on techniques of mathematical proofs. Mathematical topics include the fundamental theories of sets, functions, relations, and elementary enumerative combinatorics (the sum and product rules, an introduction to permutations and combinations, and the binomial coefficients). This course will also involve the students in the writing and presenting of mathematical proofs. Thus, the assignments are expected to incorporate proper grammar, spelling, punctuation, and so forth.
* It is an enormous material to be covered, so do not fall behind.
* If it is necessary, there will be verbal updates of this handout.
* Good Luck ! I hope you will all make good grades!

SYLLABUS – MA 1025 – Introduction to Mathematical Reasoning, Summer 2014 Dr. Pante Stanica

SYLLABUS – MA 1025 – Introduction to Mathematical Reasoning, Summer 2014
Dr. Pante Stanica