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Table of contents
- THE APOSTOLIC AGE
- Download Mathematical Explorations For The Christian Thinker 2014
- God In Mathematics
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A Mathematical Journey The Joy of Thinking is a course about fun, aesthetics, and mystery—about great mathematical ideas that arise from puzzles, observations of everyday life, and habits of curiosity and effective thinking. The choice involves a question of chance that has been the source of many heated arguments.
You explore the mathematics that prepares you for future game-show stardom and explains a paradoxical example of probability. Coincidences are striking because any particular one is extremely improbable. However, what is even more improbable is that no coincidence will occur. You see that finding two people having the same birthday in a room of 45 is extremely likely, by chance alone, even though the probability that any particular two people will have the same birthday is extremely low. One of the most famous illustrations of randomness is the scenario of monkeys randomly typing Hamlet.
Another, called "Buffon's needle," shows how random behavior can be used to estimate numbers such as pi. Physicists discovered that a similar needle-dropping model accurately predicts certain atomic phenomena. The Fourth Dimension Mathematical thinking leads not only to insights about our everyday lives and everyday world but also points us to worlds far beyond our own. Fractals Or take a world that we can see: the two-dimensional realm.
Life Lessons As Professors Burger and Starbird lead you through these and other examples, you pick up some valuable life lessons: Just do it. If you're faced with a problem and you don't know how to solve it, begin by taking some action. Make mistakes and fail but never give up. Mathematicians are supremely gifted at making mistakes. The key is to use the insight from your mistakes to identify the features of a correct solution to your problem. Keep an open mind. If we are never willing to consider new ideas, then we can never hope to increase our understanding of the world around us.
Explore the consequences of new ideas. This strategy pushes us to see where an idea leads and in this way to discover new ideas and insights. Seek the essential. One of the biggest obstacles in solving real-world problems is the noise and clutter of irrelevant issues that surround them. Understand the issue. Identifying and clarifying the problem to be solved in a situation is often a significant step in reaching a solution. Understand simple things deeply.
We can never understand unknown situations without an intense focus on those aspects of the unknown that are familiar. The familiar, in other words, serves as the best guide to the unfamiliar. Break a difficult problem into easier ones. This strategy is fundamental to mathematics and, indeed, applicable in everyday life.
Examine issues from several points of view. We can, for example, gain new insights by looking at the construction of an object, rather than the object itself. Look for patterns. Similarities among situations and objects that are different on the surface should be viewed as flashing lights urging us to look for explanations. Patterns help us to structure our understanding of the world, and similarities are what we use to bring order and meaning to chaos. The Un-Math Math This is probably not like the mathematics you had at school.
How can we see the fourth dimension in a Salvador Dali painting?
THE APOSTOLIC AGE
Hide Full Description. Average 30 minutes each. A way to refine our worldview is to become more precise in describing what we see. Each of the classical theories of numbers, geometry, topology, fractals, and probability offer tools. Numbers accompany us throughout our lives and play a fundamental role in the realm of mathematics.
By counting and quantifying, we understand our world with more refinement. To a mathematician, numbers have their own personalities. This lecture explores the ways they have been used and understood—and have captivated humankind—through the ages. We see how a hidden order of numbers actually underlies much of nature's beauty, and explore the remarkable insights available in the pattern known as Fibonacci numbers.
A potent method for discovering new insights is to isolate and examine patterns—a process that leads us to the most pleasing proportion in art and architecture: the Golden Mean. We investigate our newly honed sense of mathematical aesthetics to see how it illuminates the structure behind aesthetically pleasing art and architecture to arrive at a new appreciation for what is known as the Golden Rectangle.
Download Mathematical Explorations For The Christian Thinker 2014
Why, exactly, is the Golden Rectangle so visually appealing? A surprising property may hold the answer. The Pythagorean Theorem perhaps best represents all of mathematics, and we examine some of its most elegant proofs, along with the alluring relationship between the conic section and the ellipse. Symmetry and regularity lie at the heart of classical beauty. The five regular, or Platonic, solids embody not only elegant symmetry but also an elegant duality in their nature. For millennia, the five Platonic solids inspired thinkers with a mystical allure.
Kepler mistakenly thought they explained the orbits of the then-known planets. But planets aren't involved, as we see when we discover why there are only five Platonic solids. Though the fourth dimension lies beyond our daily experience, understanding is within our reach, and we can visualize and explore it by using our knowledge of familiar realms and arguing by analogy. We consider the geometry of the fourth dimension, beginning with artistic works inspired by dimension, then building and visualizing our own four-dimensional cube.
Must every surface have two sides?
Surprisingly, the answer is no. Though a single-sided surface with no edge at all cannot be constructed entirely in three-dimensional space, it can be effectively described and modeled, as illustrated by the elegant surface of the Klein bottle. Even the act of folding a piece of paper can be the gateway to a rich trove of nuance, introducing us to the idea of fractals and showing how patterns and structure can emerge from seemingly unpredictable "randomness.
Our simple paper-folding sequence leads us not only to the secrets of the dragon curve fractal, but to an example of the classic computational theory of automata developed by Alan Turing, the father of modern computing. What does it mean to speak of an infinitely detailed image? We look at what is possible by repeating a simple process infinitely and then reasoning about the result, producing images that illustrate the ideas of self-similarity and symmetry.
We examine how chance, with some simple rules, leads us to an infinitely intricate world of fractals, which quite possibly overlaps with our own physical world. The uncertain and unknown are not forbidding territories into which we dare not tread. Instead, they can be organized and understood as we construct a means to measure the possibilities for an undetermined future. This lecture shows us how to put a number to the possibilities of the unknowable future as it examines the quantitative measure known as expected value and how it can be used.
Coincidences and random behavior do occur, often with predictable frequency. This lecture takes a look at randomness and how the principles of probability help us to understand it better. Coincidences are so striking because any particular one is extremely improbable. But what is even more improbable is that no coincidences will occur. We examine why. This final lecture looks at 10 "lessons for life" that can be drawn from a range of mathematical themes and concepts.
Clone Content from Your Professor tab. What Does Each Format Include? Standard carrier data rates may apply in areas that do not have wifi connections pursuant to your carrier contract. Professor 1 of 2 Michael Starbird, Ph. Professor 2 of 2 Edward B. Burger, Ph. He received his B. Mathematics from the Visual World. What Are the Chances? Probability Made Clear. Meaning from Data: Statistics Made Clear.
God In Mathematics
Set What Are the Chances? Edward B. He graduated summa cum laude from Connecticut College, where he earned a B. He earned his Ph.