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Numbers - Less-than and Greater-than

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Data Science Math Skills

듀크대학교

4.5(4,670개의 평가) | 140K명의 학생이 등록함

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Data science courses contain math—no avoiding that! This course is designed to teach learners the basic math you will need in order to be successful in almost any data science math course and was created for learners who have basic math skills but may not have taken algebra or pre-calculus. Data Science Math Skills introduces the core math that data science is built upon, with no extra complexity, introducing unfamiliar ideas and math symbols one-at-a-time. Learners who complete this course will master the vocabulary, notation, concepts, and algebra rules that all data scientists must know before moving on to more advanced material. Topics include: ~Set theory, including Venn diagrams ~Properties of the real number line ~Interval notation and algebra with inequalities ~Uses for summation and Sigma notation ~Math on the Cartesian (x,y) plane, slope and distance formulas ~Graphing and describing functions and their inverses on the x-y plane, ~The concept of instantaneous rate of change and tangent lines to a curve ~Exponents, logarithms, and the natural log function. ~Probability theory, including Bayes’ theorem. While this course is intended as a general introduction to the math skills needed for data science, it can be considered a prerequisite for learners interested in the course, "Mastering Data Analysis in Excel," which is part of the Excel to MySQL Data Science Specialization. Learners who master Data Science Math Skills will be fully prepared for success with the more advanced math concepts introduced in "Mastering Data Analysis in Excel." Good luck and we hope you enjoy the course!

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배우게 될 기술

Bayes' Theorem, Bayesian Probability, Probability, Probability Theory

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4.5(4,670개의 평가)

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PS

Jul 23, 2017

This is neat little course to revise math fundamentals. I generally find learning probability a little tricky. This course helped me a lot in better understanding Bayes Theorem. Thank you professors.

MG

Mar 28, 2018

Please include integration, algorithm analysis (big O, theta, omega), recursion and induction. Your course is helpful, thank you. If you add those things I've mentioned it would be absolute gold.

수업에서

Building Blocks for Problem Solving

This module contains three lessons that are build to basic math vocabulary. The first lesson, "Sets and What They’re Good For," walks you through the basic notions of set theory, including unions, intersections, and cardinality. It also gives a real-world application to medical testing. The second lesson, "The Infinite World of Real Numbers," explains notation we use to discuss intervals on the real number line. The module concludes with the third lesson, "That Jagged S Symbol," where you will learn how to compactly express a long series of additions and use this skill to define statistical quantities like mean and variance.

Numbers - The Real Number Line9:55

Numbers - Less-than and Greater-than6:37

Numbers - Algebra With Inequalities10:01

Numbers - Intervals and Interval Notation7:58

강사:

Daniel Egger
Executive in Residence and Director, Center for Quantitative Modeling
Paul Bendich
Assistant research professor of Mathematics; Associate Director for Curricular Engagement at the Information Initiative at Duke

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스크립트

Okay, welcome back everyone. We're going to start a few video series on the idea of inequalities. And this video it's just going to give you a short one. It's going to give you the basic idea. The whole point here is to introduce you to symbols like a < b, x > y, c is less than or equal to d, z is greater than or equal to w, and this really funny one down here, which we often say, e << f. The first four of these are really well-defined mathematical concepts, the other one is a bit fuzzy, but you'll see it throughout all data science, so we really need to name it here. Let's start from the top and draw a real number line. And suppose here's 0, here's the number 2, here's the number 3.1, and let's consider this statement. 2 < 3.1. This funny little pacman symbol here pointing that way is read, is less than. So here's a statement, let's think about what the statement means and see why it's true. This statement, 2 < 3.1 means, 2 is to the left. Of 3.1 on the real number line, r, which is in fact true, 2 is the left of 3.1. Let's say 11.78 < 3.1, say it's about there. Fact, 11.78 is also to the left of 3.1 on the number line. So, in general, when I write A less than B, I mean A, wherever it is on the real number line. And I want to put and pick a B to make that true. B has to be somewhere over here. So A has to be to the left of B. A common misconception is that when you say A < B, say that means literally A is smaller than B. That actually works when A and B are both positive. Somehow 2 is smaller than 3.1 by the plain English meaning, but I would not say by plain English meaning that -11.78 is smaller than 3.1. It's really just to the left of it. When we write something like 3.1 > 2, this just means 3.1 is to the right of 2 on the real number line. Which is true. In fact, A < B is true if and only if, so this is a fun little mathematical symbol for if and only if, B > A. Okay, so we've really figured out what less than means, and what greater than means. Here's this funny symbol, x << y. And you actually never see this in a proper math textbook, because it's not really a proper mathematical concept. But you'll see this all the time in data science. What this really means, this means, x is much, much less than y. So for example, 1 << 1,000,000, might be a reasonable thing. I'd say reasonably not true. There's no real way for a judge to judge whether this is true or false. Whereas a statement like 2 < 3.1, you can say is that true or false. It's more much, much less. It's kind of in the eye of the beholder, but we tend to agree what it means. Somehow, 1,000,000 towards one, and that's also very important. Okay, so we figured out what A < B means, let's think about less than or equal to. So this statement a, I'm going to make this funny symbol. So this read, less than or equal to. First just in terms of writing, the way you write this is you first write the less than sign and then you put one line under there. And sometimes you really should put two for less than or equal to, and every now and then you'll see that, that a is less than and then the equals sign of b. But almost always you see less than and one line under it. What does this mean? This means that a < b, or a = b. It's literally just a shorthand in terms of the real number line. If this is b here, a less than or equal to b, means either a is less than b, which means a is somewhere here to the left of b or a is plopped right on top of b, and a equals b. Okay, fine. So how do we check if a claim, like a is less than or equal to b is true, if someone gives us specific examples? Let's see. So suppose someone proposed to me that 2 is less than or equal to 3.1. Do we believe them? Well, that person's really saying that at least one of two claims is true. This means that, 2 < 3.1, or 2 = 3.1. The first of these claims is true. The second claim is false, but taken together the claim is true. That's the nice thing about or you only need to satisfy one requirement. Say on the other hand someone claims that 2 is less than or equal to 2. So that means that the person says either, 2 < 2, or 2 = 2. First one's false. Second one's true. Taken together, they're true. And let's take one where we lose. Suppose that someone wants to say that 2 is less than or equal to 0.8. This means that either, 2 < 0.8, or 2 = 0.8. First one of these is false, the second one is false, and so we don't win. It's false overall. Okay, that concludes the video on basic inequalities. We've learned what less than means, greater than, less than or equal to, and greater than or equal to, all of which are proper mathematical concepts. We've also learned what it means to say that A << B, which is not a proper mathematical concept, but it's an intuitive one people use a lot. And that concludes our video for today.

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