Syllabus for College Now Discrete Mathematics, MAT 237
Professor Sormani, Lehman College, CUNY
Mondays and Wednesday 4:05-5:55pm Gillet 333:
First class Sept 11, last class Dec 13, no meeting Oct 2 and Oct 9, final Dec 20
Topics:
Set theory, Quantifiers, Intersections, Unions , Complements,
applications to solving inequalities, cartesian products,
logic, truth tables,
direct proofs, proof by contradiction, proof by induction,
how to approach proving, disproof by counter example, quantifiers,
functions, injectivity, surjectivity, inverses, restricted domains,
applications to trigonometric and exponential functions,
induction, cardinality, summation notation,
combinatorics, Fibanacci numbers, permutations, binomial theorem,
discrete probability, Graph Theory and Trees
Text: Rosen
Discrete Mathematics and its Applications,
McGraw Hill, 6th Edition
(pick up at 189 Carmen Hall before Wed class)
This turned out to be a very poor choice of textbook for this class. Supplies: A spiral notebook of graph paper for notes.
A cheap scientific calculator with buttons for sin, cos, tan,
Ln, and Log.
Homework:
This includes reading the appropriate section of the textbook
and doing the assigned problems. For proofs, please number
each step and justify every statement refering specificly
to hypothesis and prior steps or theorems in the textbook.
Working with study partners can make homework easier and more fun.
You may also email me questions: sormanic@member.ams.org
Special graded homework projects are part of the final grade.
Grading: Exam I is 15%, Exam II is 15%, Classwork is 5%, Homework is 35%. The final is 30% of the grade.
Syllabus:
Mon Sept 11: Review of Precalculus No homework.
Wed Sept 13: Review of Precalculus Review your precalculus notes.
Mon Oct 2: No meeting, Yom Kippur HW: Hand in Homework from last wednesday on Wed Oct 4
Wed Oct 4: Review Session homework deadline moved to Wed Oct 11 It is ok if the homework is difficult and you cannot complete it!
Mon Oct 9: No meeting, Columbus Day HW: Hand in *ed problems from last Wednesday on Wed Oct 11
Wed Oct 11: Rules of Inference and Sets (1.6 and 111-115,119) HW: 1.6/1*,6*,9*,13*,21,15*; 2.1/1*,2ab*,4,13,29,33*,35*
Mon Oct 16: Cartesian Products and Set Operations (2.1,2.2) HW: 2.1/7,22,29,34, 2.2/3,6b,12,23,25a, 26a, 45
Wed Oct 18: Functions (2.3) HW: 2.1/23,31,36, 2.3/1,7a,10,11,15a,19ab,30,47a,75a
Mon Oct 23: Sequences and Summations (2.4) HW: 2.4/3a, 7, 9cdf, 13abcd, 31bc, 42
Wed Oct 25: Proof by Cases (1.7) amd Algorithms (3.1 pages 167-173) HW: 3.1/3,6,7,10,15, 1.7/5,12,16,33, 2.4/32cd, 36,37
hand in on Monday, circling 2 from 3.1 and 2 from 1.7 that
you think are correct, put question marks next to ones you
are unsure of.
Mon Oct 30: Algorithms (3.1) HW: 3.1/3,6,7,10,15,43,
Wed Nov 1: Mathematical Induction (4.1) 4.1/ 3abcdef,15, 79 due Wed Nov 8 warning do 3 right away.
Study for the Exam Assuming that you already understand and have completed
all the homework from Chapters 1 and 2 (including 1.7), you
need only spend about 4 hours studying the following examples
(spend 2 hours reviewing them on Friday, then 2-3 hours trying
to solve them yourself on Saturday and Sunday). The exam will
have 9 problems each as difficult as one of these examples.
1.2/Ex2,Ex3,Ex4 1.3/Ex8,Ex9,Ex11,Ex14,Ex15,Ex16,
1.3/Ex21,Ex22, 1.4/Ex3,Ex4,Ex14, 1.6/Ex1,Ex11,Ex15,
1.7/Ex3,Ex13, 2.1/Ex16, 2.2/Ex1,Ex3,Ex11,Ex12,
2.3/Ex9,Ex10,Ex12,Ex13, 2.4/Ex1,Ex2,Ex9,Ex10,Ex11
If you have not yet understood all the homework in
a section it will take you longer to study the examples
in that section and you may have to read quite a bit of
the section before understanding the example.
Please remember to sleep the night before the exam.
Sleep helps you process your memory and will prevent blackouts
during the exam.
Mon Nov 6: Exam I on Chapters 1-2 HW due Wed: read 4.1/ex1,ex2,ex3, do 4.1/3abcdef,15,79
Wed Nov 8: Growth of Functions (3.2) Homework to hand in on Monday:
Read part of 2.3: pages 136-138. Do problem 9 from the exam, and 2.3/69
Read all of 3.1. Do 3.1/3,23,24.
Read part of 3.2: pages 180-186 Do 3.2/1,3
Mon Nov 13:
Recursive Definitions and Algorithms (4.3-4.4) HW due Monday (on the next exam): 4.3/ Read 294-297 Do 1a,2a,7,13
4.4/ Read 311-312 Do 1, Read 170-171, Read 314, Do 7,8,
Read 316-317, Do 28,29,30
Wed Nov 15: Counting (5.1) Prof StJohn HW: complete the above work
Mon Nov 20: Permutations and Combinations and Binomial Theorem (5.3-4) HW due Nov 27 broken into 3 work sessions:
Read 5.1/ Ex 1, Ex 2, Ex 4, Ex17, Do 5.1/3, 7,8,9
Read 5.3/pages 355-359, Do 5.3/9,11a,13,15,17,19,23
Read 5.4/page 363-364, pages 366-367, Do 5.4/1,5,7,9
Warning: the next exam includes Algorithms and Induction
so be sure to hand in old homework from Nov 6 and Nov 13
on Monday as well so I have time to grade it.
Wed Nov 22: no class, Thanksgiving! HW: do the above assignment
Mon Nov 27:Discrete Probability (6.1) HW: Read 6.1/ Ex2, Ex4, Ex7; Do 6.1/1,3,5,7,25a,29,33a; check your answers
in the back of the book
Wed Nov 29: Review for the Exam HW:
Mon Dec 4: Exam II on Chapters 3.1, 3.2, 4.1, 4.3, 4.4, 5.1, 5.3, 5.4 The exam will require you to construct algorithms, write proofs by induction
and do a number of short questions from Chapters 5 and 6.
Algorithms: 3.1/read and understand all the algorithms (pretend to be the computer)
4.3/read 294-297 4.4/read and understand all algorithms on pages 311-312, 316-317, 170-171
Then on another day, practice writing those algorithms and check against the text.
Proofs: understand: 1.6/ex1,ex11,ex15 1.7/ex3,ex13, practice: 4.1/ ex1,ex2,ex3
Then on another day, practice writing those proofs and check against the text.
Combinatorics: this will be short answer similar to SAT questions:
Read 5.1/ Ex 1, Ex 2, Ex 4, Ex17, Read 5.3/pages 355-359,
Read 5.4/page 363-364, pages 366-367, Read 6.1/ Ex2, Ex4, Ex7;
Practice all these examples again and check against the book.
Wed Dec 6: Graphs and the Konigsberg Bridge Problem
(9.1, 9.2,9.5) Prof. Jung There is no time to catch up on old homework! HW: Do Proofs by Induction: 4.1/6,18,38,40,
Prepare for a counting and probability exam on Wednesday
Read 5.1/ Ex 1, Ex 2, Ex 4, Ex17, Read 5.3/pages 355-359,
Read 5.4/page 363-364, pages 366-367, Read 6.1/ Ex2, Ex4, Ex7;
Mon Dec 11: Trees and Tic-Tac-Toe (10.1-2) Prof. Rosholt Prep for counting and probability exam on Wed.
Wed Dec 13: Review for the Final: which will include graphs and trees
Logic and Proofs: 1.2/Ex2,Ex3,Ex4 1.3/Ex8,Ex9,Ex11,Ex14,Ex15,Ex16,Ex21
1.4/Ex3,Ex4, 1.6/Ex1,Ex11, 1.7/Ex3,Ex13, 4.1/Ex1,Ex2,Ex3
Set Theory and Functions:
2.1/Ex16,Ex19,Ex20 2.2/Ex1,Ex3,Ex5,Ex12,Ex15,Ex16,Ex17
2.3/Ex9,Ex10,Ex12,Ex13, 2.4/Ex1,Ex2,Ex9,Ex10,Ex11, Ex12
Combinatorics and Probability:
5.1/ Ex1,Ex2,Ex4,Ex17, Read 5.3/pages 355-359,
Read 5.4/page 363-364, pages 366-367, Read 6.1/ Ex2, Ex4, Ex7;
Graphs and Trees:
9.2/Ex1, 9.5/read pages 633-634, 10.1/Ex1, Ex4, 10.2/Ex3,Ex7