Zero to Infinity: A History of Numbers (The Great Courses)

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Numbers surround us. They mark our days, light our nights, foretell our weather, and keep us on course. They drive commerce and sustain civilization. But what are they? Whether you struggled through algebra or you majored in mathematics, you will find Professor Edward B. Burger’s approach accessible and stimulating. If you think math is just […]

Zero to Infinity: A History of Numbers (The Great Courses)

zane 0 Comments

Numbers surround us. They mark our days, light our nights, foretell our weather, and keep us on course. They drive commerce and sustain civilization. But what are they? Whether you struggled through algebra or you majored in mathematics, you will find Professor Edward B. Burger’s approach accessible and stimulating. If you think math is just […]

Introduction to Number Theory (The Great Courses)

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How could an ancient king be tricked into giving his servant more than 671 billion tons of rice? It’s all due to a simple but powerful calculation involving the sum of geometric progression — an important concept in number theory and just one of the fascinating concepts you’ll encounter in An Introduction to Number Theory. […]

Vectors and spaces (Khan Academy)

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Let’s get our feet wet by thinking in terms of vectors and spaces. (1) Vectors Vector intro for linear algebra Real coordinate spaces Adding vectors algebraically & graphically Multiplying a vector by a scalar Vector examples Scalar multiplication Unit vector notation Unit vectors Add & subtract vectors Add vectors: magnitude & direction to component Parametric […]

Derivative applications (Khan Academy)

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The reason we study calculus, and the reason it was invented, is for its many uses in real-world problems. In particular, derivatives let us optimize functions and study their rates of change. Here we cover optimization, rates of change, L’Hopital’s rule, the mean value theorem, and more! (1) Equations of normal and tangent lines Equation […]

Random variables and probability distributions (Khan Academy)

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Random variables. Expected value. Probability distributions (both discrete and continuous). Binomial distribution. Poisson processes. (1) Random variables and probability distributions Random variables Discrete and continuous random variables Constructing a probability distribution for random variable Constructing probability distributions Probability density functions (2) Expected value Expected value Term life insurance and death probability Getting data from expected […]

Rational and irrational numbers (Khan Academy)

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Learn about irrational numbers and how to identify them. (1) Irrational numbers Intro to rational & irrational numbers Classifying numbers: rational & irrational Classify numbers: rational & irrational Classifying numbers Classify numbers (2) Proofs concerning irrational numbers Proof: √2 is irrational Proof: square roots of prime numbers are irrational Proof: there’s an irrational number between […]

Quadratic equations and functions (Khan Academy)

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Learn how to solve quadratic equations, and how to analyze and graph quadratic functions. (1) Solving quadratic equations by taking square root Solving quadratics by taking square roots Solving quadratics by taking square roots Solving quadratics by taking square roots examples Solve quadratic equations by taking square roots Solving quadratics by taking square roots: strategy […]

Systems of linear equations (Khan Academy)

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Learn how to interpret solutions to systems of linear equations and solve them. (1) Introduction to systems of linear equations Systems of equations: trolls, tolls (1 of 2) Testing a solution to a system of equations Test solutions to systems of equations (2) Graphical representation of systems of equations Systems of equations: trolls, tolls (2 […]

Functions (Khan Academy)

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Functions are mathematical entities that assign unique outputs to given inputs. Sounds simple? Think again! In this topic you will evaluate, graph, analyze, and create various types of functions. (1) Introduction to functions What is a function? (2) Evaluating functions Evaluating a function: formula Evaluate functions Evaluate a function: graph Evaluate functions from their graph […]