ࡱ> ?A>a bjbj <-AbAbx: : 8D'fZZZZZ555F'H'H'H'H'H'H'$-)+l'55555l'ZZ'5ZZF'5F'r%T&Z,~|&2''0',&y,3y,&y,&h5555555l'l'555'5555y,555555555: B |:  GROSSMONT COLLEGE Official Course Outline MATHEMATICS 245 DISCRETE MATHEMATICS 1. Course Number Course Title Semester Units Semester Hours MATH 245 Discrete Mathematics 3 3 hours lecture: 48-54 hours 96-108 outside-of-class hours 144-162 total hours 2. Course Prerequisites A C grade or higher or Pass in Math 280 or equivalent. Corequisite None Recommended Preparation None. 3. Catalog Description Introduction to discrete mathematics. Topics to include sets, relations, summations, elementary counting techniques, recurrence relations, logic, and proofs. This course is appropriate for mathematics and computer science majors. 4. Course Objectives The student will: a. Simplify and evaluate basic logic statements including: compound statements, implication, inverse, converse, contrapositive, predicates, and quantifiers. b. Apply methods of proof including: direct and indirect proofs, proof by cases, and mathematical induction. c. Demonstrate knowledge of elementary number theory including: modular arithmetic, prime numbers, GCD, and summation formulas. d. Analyze discrete mathematical relations and functions using elementary set theory. e. Solve counting problems by applying elementary counting techniques including: the product and sum rules, permutations, combinations, the pigeon-hole principle, and binomial expansions. f. Solve problems using recursion and recurrence relations. 5. Instructional Facilities Standard classroom equipped with: a. Whiteboards b. Overhead projector/document camera c. SmartCart 6. Special Materials Required of Student Scientific calculator. MATHEMATICS 245 DISCRETE MATHEMATICS page 2 7. Course Content a. Basic logic: compound statements, truth tables, DeMorgan's laws, implication, inverse, converse, contrapositive, predicates, quantifiers. b. Methods of proof: argument forms, direct proof, proof by cases, proof by contradiction, mathematical induction. c. Sequences, subscript notation. d. Elementary number theory: modular arithmetic, prime numbers, GCD, summation notation, simple summation formulas. e. Set theory: basic definitions, Venn diagrams, Cartesian product, power sets. f. Elementary counting: Product rule, sum rule, permutations, combination, binomial theorem. g. Functions, pigeon-hole principle. h. Recursion and recurrence relations. i. Relations: reflexive, symmetric, and transitive properties, equivalence relations, partial orders, linear orders. g. Historical contributions to the development of number theory from diverse cultures. 8. Method of Instruction The development of problem solving techniques may be achieved by using a variety of instructional techniques including instructor presented examples, individual and group work, and daily problem assignments. 9. Methods of Evaluating Student Performance a. Homework. b. Independent exploration activities. c. Class participation/problem presentations. d. Quizzes. e. Tests. f. In-class final exam (comprehensive). 10. Outside Class Assignments a. Homework. b. Take-home tests c. Problem sets. 11. Texts a. Required Text(s): Epp, Susanna S. Discrete Mathematics with Applications. Belmont, CA: Cengage Learning, 4th edition, 2011. b. Supplementary texts and workbooks: None. Addendum: Student Learning Outcomes Upon completion of this course, our students will be able to do the following: Evaluate and simplify basic logic. Define and apply the concepts from elementary number theory and elementary set theory. Apply direct and indirect methods of proof. Solve counting problems. Date approved by the Governing Board: December 11, 2012   ,.V[hiuv   + - h i t z { } ɾɶɾxht`h)OJQJht`h,OJQJht`h,>*OJQJ^Jht`h,OJQJ^Jht`hdOJQJ^JhdOJQJht`h^`OJQJh^`OJQJht`h|">*OJQJht`hd>*OJQJht`h?c>*OJQJht`hdOJQJ/-./VW , - h  d*$^ d*$  zd*$gd^`  zd*$gd^`  `x$d*$ 'd*$ d*$ d*$h i u v { | j [ p   !@&(|d*$^`| Dd*$^`D d*$ d*$^p ,:qqT T|d*$^`|gd) T*d*$^*`gd) *T*d*$^*`gdd *T*d*$^*` T|d*$^`|  !@&(|d*$^`| ,0:;Afiu16KL#LGNSm~ />fwxy{|~ݭꛗ h 7CJjh 7Uh 7jh 7CJUht`OJQJht`hd>*OJQJ^Jht`hdOJQJht`h)dOJQJht`hd>*OJQJht`hdOJQJ^Jht`hdOJQJht`h)OJQJ2:=ghUx  * !@&(*d*$^*` 'd*$ Td*$gd^` Td*$gdd T|d*$^`|   !@&(d*$gd  Uc:b12LMz TDd*$^`D *TDd*$^`Dgdd T|d*$^`|  * !@&(d*$  * !@&(*d*$^*`MN\"6IJTUk   T|d*$^`|gdd T|d*$^`| /0%>?xz{}~d Td*$gdd & F 1$^`gdd ^gddgdd T|d*$^`|gdd T|d*$^`|gdd:....()()))()00P8$BP/ =!8"8#8$%88 Dp"s2 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p8XV~ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@_HmH nH sH tH D`D Normal1$OJQJ_HmH sH tH DA D Default Paragraph FontViV  Table Normal :V 44 la (k (No List 8+8  Endnote TextCJ>* > Endnote ReferenceH*::  Footnote TextCJ@& !@ Footnote ReferenceH*NN TOC 1) $ 0*$]^`0JJ TOC 2% $ 0*$]^`0JJ TOC 3% $ p0*$]^p`0JJ TOC 4% $ @ 0*$]^@ `0JJ TOC 5% $ 0*$]^`0BB TOC 6 $0*$^`0:: TOC 70*$^`0BB TOC 8 $0*$^`0BB TOC 9 $ 0*$^`0N N Index 1% $ `*$]^``N N Index 2% $ 0*$]^`0>.>  TOA Heading *$ $.". CaptionCJ:/: _Equation CaptionHH ;7 Balloon Text!CJOJQJ^JaJPK![Content_Types].xmlN0EH-J@%ǎǢ|ș$زULTB l,3;rØJB+$G]7O٭Vc:E3v@P~Ds |w< ,  h p :U  8@0(  B S  ?it09c d m p xz{}~@KHS# . | x333333333gz /0;;iu fw{L!DDEbO*vAko4f6^~Ķ0^`0o(.^`.L^`L.  ^ `.[[^[`.+L+^+`L.^`.^`.L^`L. 0 ^ `0o(.rr^r`.B LB ^B `L.  ^ `.^`.L^`L.^`.RR^R`."L"^"`L.^`o(.rr^r`.B LB ^B `L.  ^ `.^`.L^`L.^`.RR^R`."L"^"`L.h ^`hH.h ^`hH.h pL^p`LhH.h @ ^@ `hH.h ^`hH.h L^`LhH.h ^`hH.h ^`hH.h PL^P`LhH.vAkDEb{L!6^~؎[        4,         RT                  "5* 7;!t\)dmwQd?cZ,{t`|"d^`,)xz@@UnknownG.[x Times New Roman5Symbol3. .Cx Arial71 Courier5..[`)TahomaA$BCambria Math"9)F$ GJzgtf(P (P )P4qq2Q)PHP?5T2!xxYGg= !A Course Outline Template [blank]GCCCDBarbara Prilaman    Oh+'0 0< \ h t $A Course Outline Template [blank]GCCCD Normal.dotmBarbara Prilaman4Microsoft Office Word@G@L @\@nZ~(P  ՜.+,0 px  GCCCDAq "A Course Outline Template [blank] Title  !"#$%&'()*+,-/012345789:;<=@Root Entry F?~B1Table,WordDocument<-SummaryInformation(.DocumentSummaryInformation86CompObjr  F Microsoft Word 97-2003 Document MSWordDocWord.Document.89q