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Calculus. Free e-books and e-lectures on Algorithms, Math, and Cryptography. Electrical Engineering and Computer Science. Math21b, Fall 2003, Linear Algebra and Differential Equations. Calculus - Exampleproblems. Math Help - SolveMyMath. The momentum representation. How to Calculate a Square Root by Hand: 21 steps (with pictures) Edit Article CalculatorUsing Prime FactorizationFinding Square Roots Manually Edited by NatK, Maluniu, Luís Miguel Armendáriz, Webster and 44 others In the days before calculators, students and professors alike had to calculate square roots by hand.

Several different methods have evolved for tackling this daunting process, some giving a rough approximation, others giving an exact value. To learn how to find a number's square root using only simple operations, see Step 1 below to get started. Ad Steps Method 1 of 2: Using Prime Factorization 1Divide your number into perfect square factors. Method 2 of 2: Finding Square Roots Manually. Free Maths Video Lecture courses. Touch Mathematics. Mathematics reference: Rules for differentiation. An Interactive Guide To The Fourier Transform. Pauls Online Math Notes. Mathematics Applied to Physics/Engineering. Why Does e^(pi i) + 1 = 0? This page is just a collection of a couple of answers on the LiveJournal Mathematics Community in a thread about eπi + 1 = 0.

Why Does e^(pi i) + 1 = 0?

Soon, I will whip them into a more coherent form. In collegiate calculus, you probably learned about something called Taylor series. You can use Taylor series to make polynomial approximations of infinitely-differentiable functions. If you take the Taylor series out infinitely, you actually have the function. The general form for a Taylor series is this: ∑ f(n)(x0) * (x - x0)n / n! Where the sum goes from n=0 to n=infinity and f(n)(x0) means the n-th derivative of f(x) evaluated at x0. Also, note that f(0)(x) is just f(x). Graduate Program in Mathematics, Study guides for Comp Exams, University of Illinois at Urbana-Champaign. Demystifying the Natural Logarithm (ln) After understanding the exponential function, our next target is the natural logarithm.

Demystifying the Natural Logarithm (ln)

Given how the natural log is described in math books, there’s little “natural” about it: it’s defined as the inverse of e^x, a strange enough exponent already. But there’s a fresh, intuitive explanation: The natural log gives you the time needed to reach a certain level of growth. Main Page - Exampleproblems. Untitled. Two by Two. Essentially the technique converts the first factor into binary, multiplies each of its constituents by the second factor, and sums the results.

Two by Two

Imagine that each line is associated with a power of 2: the first line with 20, the second with 21,and so on. The business in the first column, halving the first factor successively and crossing out those lines with even numbers, effectively reduces the first factor to its binary constituents — here, the lines that remain are those associated with 20, 25, and 26, and, sure enough, 20 + 25 + 26 = 97. The Thirty Greatest Mathematicians. Click for a discussion of certain omissions.

The Thirty Greatest Mathematicians

Please send me e-mail if you believe there's a major flaw in my rankings (or an error in any of the biographies). Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different. I'm sure I've overlooked great mathematicians who obviously belong on this list. Please e-mail and tell me! Color Theory 101. Weekly wanderings through higher math—from not so high a vantage point.

Calculus. Intuitive Understanding Of Euler’s Formula. Geometry. The word geometry is Greek for geos - meaning earth and metron - meaning measure.


Geometry was extremely important to ancient societies and was used for surveying, astronomy, navigation, and building. Geometry, as we know it is actually known as Euclidean geometry which was written well over 2000 years ago in Ancient Greece by Euclid, Pythagoras, Thales, Plato and Aristotle just to mention a few. The most fascinating and accurate geometry text was written by Euclid, and was called Elements. Calculus Derivatives Cheat Sheet. What are the best rules, formulas and tricks in math? - math formulas rules. GEM1518K - Mathematics in Art & Architecture - Project Submission.

“For me it remains an open question whether [this work] pertains to the realm of mathematics or to that of art.” - M.C.

GEM1518K - Mathematics in Art & Architecture - Project Submission

Learning Calculus: Overcoming Our Artificial Need for Precision. Accepting that numbers can do strange, new things is one of the toughest parts of math:

Learning Calculus: Overcoming Our Artificial Need for Precision

Geometry Help. Looking for some Geometry Help?

Geometry Help

Our materials here review the basic terms and concepts in geometry and provide further lessons to help you develop your understanding of geometry and its applications to solving problems in real life. Geometry is about the shape and size of things. It is the study of points, lines, angles, shapes, their relationships, and their properties. Videos have been included in almost all the following topics to help reinforce your understanding. Angles Triangles Polygons Circles. No, really, pi is wrong: The Tau Manifesto by Michael Hartl. Elementary Calculus: Example 3: Inscribing a Cylinder Into a Sphere. Find the shape of the cylinder of maximum volume which can be inscribed in a given sphere.

Elementary Calculus: Example 3: Inscribing a Cylinder Into a Sphere

The shape of a right circular cylinder can be described by the ratio of the radius of its base to its height. This ratio for the inscribed cylinder of maximum volume should be a number which does not depend on the radius of thesphere. For example, we should get the same shape whether the radius of the sphere is given in inches or centimeters. Algebra Help Math Sheet. Arithmetic Operations The basic arithmetic operations are addition, subtraction, multiplication, and division.

Algebra Help Math Sheet

These operators follow an order of operation. Addition. Pascal's Triangle. Patterns Within the Triangle. Calculus and Differential Equations. A Gentle Introduction To Learning Calculus. I have a love/hate relationship with calculus: it demonstrates the beauty of math and the agony of math education. Calculus relates topics in an elegant, brain-bending manner.

My closest analogy is Darwin’s Theory of Evolution: once understood, you start seeing Nature in terms of survival. You understand why drugs lead to resistant germs (survival of the fittest). You know why sugar and fat taste sweet (encourage consumption of high-calorie foods in times of scarcity). It all fits together. Calculus is similarly enlightening. Reflections on Relativity. Mathematics Department - Mathematics Web Sites. Maths Online Courses. Ask Dr. Math - College Level Archive. English names of the first 10000 powers of 10 - American System without dashes. Mathematics Department : Mathematics Courses. The Math Guy. Visualizing Basic Algebra. Last weekend, I shared some interesting properties of numbers with my kids. The great thing about explaining something to a non-expert is that you have to actually understand the topic. (This is why making teaching universities and research universities the same actually makes sense.)

How to Become a Pure Mathematician (or Statistician) Free Mathematics Books Download Free Mathematics Ebooks Online Mathematics tutorials. Analysis index. Undergraduate contest problems and solutions. Abstract Algebra - Free Harvard Courses. Foundations of Mathematics. S Introduction to Complex Systems. Dave's short course in trigonometry. Table of Contents. Piety within Progression. ENDEAVOR SNOWBOARDS - RC SERIES Complete RC Series line. Tutorials related to Kinematic Mechanisms.