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Description
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...
Description
We commonly define the Pythagorean theorem using the formula a2 + b2 = c2. But Pythagoras himself would have been confused by that. Explore how this famous theorem can be explained using common geometric shapes (no fancy algebra required), and how it’s a critical foundation for the rest of geometry.
Description
While some statistics are deliberately misleading, others are the product of confused thinking due to Simpson's paradox and similar errors of statistical reasoning. See how this problem arises in sports, social science, and especially medicine, where it can lead to inappropriate treatments.
Description
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!
Description
Drawing on your experience solving quadratic functions, analyze the parabolic shapes produced by such functions when represented on a graph. Use your algebraic skills to determine the parabola's vertex, its x and y intercepts, and whether it opens in an upward "cup" or downward in a "cap."
Description
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.
Description
Combinatoricsis the study of counting questions such as: How many outfits are possible if you own 8 shirts, 5 pairs of pants, and 10 ties? A trickier question: How many ways are there to arrange 10 books on a shelf? Combinatorics can also be used to analyze numbering systems, such as ZIP Codes or license plates, as well as games of chance.
Description
World-renowned math educator Dr. James Tanton shows you how to think visually in mathematics, solving problems in arithmetic, algebra, geometry, probability, and other fields with the help of imaginative graphics that he designed. Also featured are his fun do-it-yourself projects using poker chips, marbles, paper, and other props, designed to give you many eureka moments of mathematical insight.
Description
Polynomial regression is a form of regression analysis in which the relationship between the independent and dependent variables is modelled as the power of a polynomial. Step functions fit smaller, local models instead of one global model. Or, if we have binary data, there is logistic regression, in which the response variable has categorical values such as true/false or 0/1.
Description
Delve into ANOVA, short for analysis of variance, which is used for comparing three or more group means for statistical significance. ANOVA answers three questions: Do categories have an effect? How is the effect different across categories? Is this significant? Learn to apply the F-test and Tukey's honest significant difference (HSD) test.
Description
While a creative statistical analysis can sometime salvage a poorly designed experiment, gain an understanding of how experiments can be designed in from the outset to collect far more reliable statistical data. Consider the role of randomization, replication, blocking, and other criteria, along with the use of ANOVA to analyze the results. Work several examples in R.
Description
Discover how to solve equations that contain radical expressions. A key step is isolating the radical term and then squaring both sides. As always, it's important to check the solution by plugging it into the equation to see if it makes sense. This is especially true with radical equations, which can sometimes yield extraneous, or invalid, solutions.
Description
Wrap up the course by looking at several fun and different ways of reimagining geometry. Explore the counterintuitive behaviors of shapes, angles, and lines in spherical geometry, hyperbolic geometry, finite geometry, and even taxi-cab geometry. See how the world of geometry is never a closed-book experience.
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