Logic is intellectual self-defense against such assaults on reason and also a method of quality control for checking the validity of your own views. But beyond these very practical benefits, informal logic—the kind we apply in daily life—is the gateway to an elegant and fascinating branch of philosophy known as formal logic, which is philosophy’s equivalent to calculus. Formal logic is a breathtakingly versatile tool. Much like a Swiss army...

Another indispensable number to learn ise= 2.71828 ... Defined as the base of the natural logarithm,eplays a central role in calculus, and it arises naturally in many spheres of mathematics, including calculations of compound interest.

Classify all different types of four-sided polygons (called quadrilaterals) and learn the surprising characteristics about the diagonals and interior angles of rectangles, rhombuses, trapezoids, and more. Also see how real-life objects—like ironing boards—exhibit these geometric characteristics.

Conclude the course by examining more types of number sequences, discovering how rich and enjoyable the mathematics of pattern recognition can be. As in previous lessons, employ your reasoning skills and growing command of algebra to find order - and beauty - where once all was a confusion of numbers.

Discover that by following basic rules on how to treat coefficients and exponents, you can reduce very complicated algebraic expressions to much simpler ones. You start by using the commutative property of multiplication to rearrange the terms of an expression, making combining them relatively easy.

So far, you’ve seen how to calculate the sine, cosine, and tangents of basic angles (0°, 30°, 45°, 60°, and 90°). What about calculating them for other angles—without a calculator? You’ll use the Pythagorean theorem to come up with formulas for sums and differences of the trig identities, which then allow you to calculate them for other angles.

Professor Benjamin begins his discussion of mathematical proofs with intuitive cases like "even plus even is even" and "odd times odd is odd." He builds to more complexproofs by existenceandinduction, and ends with a checkerboard challenge.

Discover the timeless riddles and paradoxes that have confounded the greatest philosophical, mathematical, and scientific minds in history. Stretching your mind to try to solve a puzzle, even when the answer eludes you, can help sharpen your mind and focus - and it’s an intellectual thrill!

Investigate a puzzle that defied some of the most brilliant minds in mathematics: the Monty Hall problem, named after the host of Let's Make a Deal! Hall would let contestants change their guess about the location of a hidden prize after revealing new information about where it was not.

Professor Benjamin introduces the ABCs of math appreciation: The field can be loved for itsapplications, itsbeauty and structure, and itscertainty. Most of all, mathematics is a source of endless delight through creative play with numbers.