# Cs 10a mathematical proof students will demonstrate

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CS 10A. Mathematical Proof. Students will demonstrate an understanding of mathematical proof and related concepts including: Analysis of the logical structure of mathematical proofs and derivations; Use contradictions and counter examples appropriately; Use mathematical induction.
The rudiments of ε,δ−proofs MATH 2215 Multivariate CalculusDepartmental Outline for MATH 2215Multivariate Calculus Description:Real-valued functions of several variables, limits, continuity, differentials, directional derivatives, partial derivatives, chain rule, multiple integrals, applications. Prerequisite:MATH 2212 Calculus of One Variable II or equivalent. Calculator:Students may have a scientific calculator. It is up to each instructor as to how much the students can use a calculator on tests. Texts:(Required) Calculus: One and Several Variables, 9 th Edition by Salas & Hille & Etgen, Wiley, 2003, ISBN 0-471-23120-7. SyllabusChapter 12 Sections 12.1 - 12.7 Vectors Chapter 13 Sections 13.1 - 13.5 Vector Calculus Chapter 14 Sections 14.1 - 14.6 Functions of Several Variables Chapter 15 Sections 15.1 - 15.9 Gradients and Extremes Chapter 16 Sections16.1 - 16.10 Double & Triple Integrals Chapter 17 Sections 17.1 - 17.2 Line Integrals MATH 2420 Discrete MathematicsDepartmental Outline for MATH 2420Discrete Mathematics Description:Introduction to discrete structures which are applicable to computer science. Topics include number bases, logic, sets, Boolean algebra, and elementary concepts of graph theory. Prerequisite:MATH 1220 Survey of Calculus or Math 1113 Precalculus. Calculator:Students may have a scientific calculator. It is up to each instructor as to how much the students can use a calculator on tests. Texts:(Required) Discrete Mathematics, 3 rd Edition by Susanna Epp, ITP, 2004, ISBN 0-534-35945-0. SyllabusChapter 1 Sections 1.1 - 1.5 The Logic of Compound Statements Chapter 2 Sections 2.1 - 2.4 The Logic of Quantified Statements
Chapter 3 Sections 3.1-3.4, 3.6 Elementary Number Theory and Methods of Proof Chapter 4 Sections 4.1 - 4.2 Sequences and Mathematical Induction Chapter 5 Sections 5.1 - 5.3 Set Theory Chapter 7 Sections 7.1 - 7.4 Functions Chapter 10 Sections 10.1-10.3, 10.5 Relations Chapter 11 Sections 11.1, 11.2, 11.5, 11.6 Graphs and trees If time permits, one could cover Section 10.4 (Cryptography), Chapter 12, or the omitted sections in Chapter 11. This material is optional. As a result of completing the course Discrete Mathematics, MATH 2420, students will be able to: 1. Identify logical form, form compound statements using the connectives and, or and not, determine truth tables of more general compound statements, determine whether two statement forms are logically equivalent or nonequivalent, apply De Morgan’s laws to form negations of and and or, determine whether a statement is a tautology or a contradiction, and use logical equivalences to simplify statement forms.