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“Introduction to Mathematical Thinking. Tutorial for Assignment By a denial of a statement ϕ we mean any statement equivalent to ⇁ϕ. Give a useful (and hence natural sounding) denial of each of the following statements. (a) 34,159 is a prime number. (b) Roses are red and violets are blue. (c) If there are no hamburgers,…

Introduction to Summation The purpose of this lecture is to understand what we mean by sigma notation, which we often use in statistics. Sigma is represented by this big Greek letter, which looks like a capital S with a long horizontal stroke through the middle. The goal of the lecture iS not to bombard you…

Introduction to Mathematical Thinking. Tutorial for Assignment A: There is a natural number solution to the equation x cubed equals 27. ( exists x in N ) [ x^3 =27] B: A million is not the largest natural number. There is an x in n such that x is greaterthan a million. ( exists x…

Second derivative test. Worked example recitation Critical points of functions, how to find them using the first derivatives, and how to classify them using the second derivative test. So we have a function, w, that’s a polynomial in two variables, x and y. It’s given by the following formula: w = x cubed minus 3xy…

Robot Arm Complete Then, you can do a similar analysis for y. And to save time, we’ve put this on the p set. You find that delta y is approximately equal to delta theta. This is the linear approximation step. Now that we are solving the problem. let us check our work. It is known…

How to Read Mathematical Formulas In order to understand the mechanics of mathematical formulas, it’s important tonknow the conventions regarding the order in which logical operators apply. As a quick summary, the precedence order for applying logical connectives is as follows: (forall L)..(..) (exists L) (…) Quantifiers are the words that bind tightly, that hold…

Introduction to Mathematical Thinking. Tutorial for Assignment 1. Prove or disprove the statement “ All birds can fly. “ False. Counterexample.Ostrich Starting with the premise that all birds can fly, we will prove or disprove this statement by finding a counter-example. An obvious one is the ostrich, which cannot fly. 2. Prove or disprove the…

Robot Arm Matrix Answer Which of the following values should it be? Plus 1, minus 1, or zero? OK, good. The correct answer is minus 1. Now let’s look at the top row. The top row is meant to give us the first derivative, delta x. So we will have delta L plus one delta…

Mean and Variance The main point of this lecture is to tie those concepts back into sigma notation, which is one of the main uses for summation. We’ll walk through this very slowly and unpack it for you. If we have a set of numbers X, with N numbers in them (XI to Xh) they’re…

Cartesian Plane – Distance Formula First, we will review the distance formula and then introduce some new concepts. First, the distance formula: If we have two points in the Cartesian plane, with coordinates (×1, y1) and (×2, y2), then the distance between them is given by the Pythagorean Theorem. Distance in the Plane – The…