1 / 8

MATH 370 Final Review

MATH 370 Final Review. Chapter 5-10. Know this well. Chapter 5 and 6: Counting/ Probability Basic counting P( n,r ), C( n,r ), C(n-1+r,r),… Basic probability, expected value Ch . 7: Recurrence Finding solutions Proving these are solutions Ch . 8: Relations Relation, function defs

jarvis
Download Presentation

MATH 370 Final Review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MATH 370 Final Review Chapter 5-10

  2. Know this well Chapter 5 and 6: Counting/ Probability • Basic counting • P(n,r), C(n,r), C(n-1+r,r),… • Basic probability, expected value Ch. 7: Recurrence • Finding solutions • Proving these are solutions Ch. 8: Relations • Relation, function defs • Def of R,S, A, T • Def of divides • Def of a=b mod m… • Def of Equiv Relation: RST • Def of PO: RAT • Def of comparable • Def of total order

  3. …topics to know well Ch. 9: Graphs • Special graphs: Kn, Cn, Wn, Qn, Km,n • Prove: • Bipartitite or not • Isomorphic or not • Planar or not • 9.8: Thm 1- chromatic # of planar graph ≤4 Ch. 10: Trees • Def of tree, rooted tree Basic Proof Methods • Direct proofs, utilizing definitions (ex: show R is transitive using the definition– Assume aRb and bRc. Show aRc.) • Indirect (contrapositive) and By Contradiction • Cases • Induction • Disproving, by using a counterexample

  4. Techniques to apply You won’t need to state these definitions, but be able to do: Ch. 7: • 7.5: |AUAUA|=… Ch. 8: • Matrices and digraphs and graphs • Do relations have certain properties: RSAT • Find closures • For (a,b) R4, find path length 4 in R • Maximal, minimal, greatest, least, glb, lub • Hasse • Compatible total order

  5. …Techniques to apply Ch. 9: • Thm. 2: undirected graph has an even # of odd degree • Calculate deg, deg-, deg+ • Adjacency tables and matrices • Paths • Strong and weakly connected • Counting paths of length l • Euler and Hamilton paths and circuits • Conditions for Euler paths and circuits (not for Hamilton) • Chromatic number of special graphs Ch. 10: • Determine if a tree or not • 10.3: pre, in, and postorder and Infix, prefix, postfix notation • 10.4: find spanning tree • 10.5: find minimum spanning tree

  6. Will be provided, so you can use them to calculate/ prove other things Ch. 5 • Binomial formula Ch. 7 • 7.1: ∑ari= … • 7.2: Thm 1 and 2 on how to find solutions to recurrence relations • N(P1’P2’…) formula • SοR definition; R n+1 = R n ο R; M S ο R = M R ο M S Ch. 8 • These statements will be given, so you may need to prove them: • 8.1: Thm. 1. R is transitive implies R n R • Thm. 2: 8.4: R* = U R n is the transitive closure of R • R* is transitive

  7. …Will be provided, so you can use them to calculate/ prove other things Ch. 9: • 9.2: Thm. 1 Handshaking: 2e= sum of deg(v)… • Euler: r=e-v+2 • Cor 1: If G connected, planar, simple, e≤ 3v-6 • Cor3: If G conn, planar simple, with no circuits length 3, then e≤2v-4 • Thm. 2: A graph is nonplanariff it contains a subgraphhomeomorphic to K3,3 or K5. Ch. 10: • 10.1: Thm 2: tree with n vertices has n-1 edges • Thm 3: full m-ary tree with I internal vertices contains n=mi+1 vertices • 10.1: Thm 4 (p.691): A full m-ary tree with n vertices has i=(n-1)/m internal vertices…

  8. Skip these • Ch. 6: Derangements • 8.2: databases • Any proofs in 9.6 • Proofs in ch. 10

More Related