Lecture 1 - Vineet Goyal Welcome Quantitative Skills Review...

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1 Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. & Graphs Instructor Welcome Algebra Refresher Quantitative Skills Review Program (QSRP) Welcome! (Slides available at www.andrew.cmu.edu/~vgoyal)
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2 Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. & Graphs Instructor Welcome Algebra Refresher Instructor Information 5 th year PhD candidate in Operations Research Teaching Experience: Sequencing and Scheduling - Spring 2007 TA Experience (MBA): Probability and Decision Making Statistics and Decision Making Optimization and Decision Making Optimization Methods in Finance, etc.
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3 Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. & Graphs Instructor Welcome Algebra Refresher The Broader Picture Modeling Real World Math Model Solution Satisfactory? No. Re- modeling Yes. Implementation
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4 Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. & Graphs Instructor Welcome Algebra Refresher Goals of QSRP Besides having fun… Develop (refresh) at least the minimum required level of understanding of math principles Become familiar with different math terminology and basic math modeling concepts Learn certain specific (pre-requisite) math/modeling concepts which will be useful for future courses at Tepper
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5 Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. & Graphs Instructor Welcome Algebra Refresher Syllabus Refer syllabus for discussion Questions?
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6 Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. & Graphs Instructor Welcome Algebra Refresher Algebra Defn : Field of math that deals with manipulating numbers and calculating the value of formulas/expressions Why do I care? Basis for advanced math -> math modeling Why do I care again? Math modeling -> Decision Making
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7 Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. & Graphs Instructor Welcome Algebra Refresher Algebra Refresher (Ch. 0) Operations with algebraic equations Factoring Fractions
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8 Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. & Graphs Instructor Welcome Algebra Refresher Collection of objects N N = {1, 2,…} Z Z = {…, -2, -1, 0, 1, 2,…} Q Q = set of rational numbers = a/b (b ≠ 0) a,b are integers, *Division by 0 is not defined R R = set of real numbers Rational + Irrational numbers Ex: √2 is not a rational number Real number line, coordinate, unit distance Subset
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9 Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. & Graphs Instructor Welcome Algebra Refresher Properties of Real Numbers Transitivity (=) If a=b and b =c then a=c Commutative (+, x) a+b = b+a and ab = ba Associative (+, x) a+(b+c) = (a+b)+c and a(bc) = (ab)c Inverse (-, ÷ reciprocal) a + (-a) = 0, a. a -1 = 1 Distributive ( ( ) ) a(b+c) = ab + ac
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Vineet Goyal Syllabus Eqns. & Ineqs. Funcs. &
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Lecture 1 - Vineet Goyal Welcome Quantitative Skills Review...

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