Patterns in Math and Genetics (04:17)

FREE PREVIEW

DNA carries the genetic information that determines a person's traits. Dr. Michael Neale studies genetic variations and patterns linked to human behavior using genetic studies and complex mathematics. The framework for statistics is linked to the framework for understanding genetics.

Patterns in Math and Genetics: Twins (04:48)

Identical twins are an ideal sample group for studying the role of genes in behavior. Neale and his team conduct statistical analysis on DNA patterns and behavioral data.

Math Meets Medicine (02:30)

Many mathematical concepts are a result of questioning events of everyday life. Architects and chemists use concepts from geometry and algebra. Abstraction generalizes ideas and can be applied in various ways, including more abstractions.

Math Meets Medicine: Graph Theory (03:29)

Graph theory is the study of nodes and the connections between them; it developed in Konigsberg, Germany in the 1700s. Graph theory, the main idea behind abstraction, is used in various ways throughout everyday life.

Math Meets Medicine: Kidney Transplants (05:03)

In the U.S., over 60,000 people are awaiting a kidney transplant. Dr. Dorry Segev discusses the efficient method of pairing recipients and donors. He and his wife worked together using graph theory to improve donor efficiency.

Building on Simplicity (05:53)

Mathematics is built on the idea of keeping things as simple as possible. Experts use logic to build upon the simplest useful set of rules provided by predecessors; gravity and the Big Bang theory are examples.

Building on Simplicity: Step-by-Step (04:45)

The discovery of Neptune is attributed to Newton's universal law. Newton's law contributed to other discoveries that can be found in the Solar and Heliospheric Observatory and Albert Einstein's work.

Theory and Practice (04:00)

Cryptanalyst Shannon Ostiguy breaks secret codes for the NSA and teaches classical cryptanalysis. Mathematics forms the foundation of cryptanalysis.

Theory and Practice: Code Breaking (03:54)

Bob Cowles teaches cryptanalysis at the Math and Related Sciences Camp; improvisation can lead to mathematical breakthroughs. In WWII, the German Enigma machine converted letters into complex code and vice versa. British intelligence built on Polish intelligence and cracked the code.

Theory and Practice: Security (03:10)

Cryptanalysis is an important part of online security. Dr. Keith Devlin discusses encryption.

New Math (02:12)

In the 1980s, biologists teamed up with mathematicians to apply knot theory to DNA. Digital music devices use math.

New Math: Wavelet Theory (06:21)

Wavelet theory is responsible for digital music. Devlin discusses manipulating wavelets and uses a tuning fork as an example.

Music of Mathematics (03:02)

Dr. Edward Burger discusses the role of creativity in developing a theorem. Math, science, and music operate in the context of common principles.

Music of Mathematics: Shared Concepts (06:21)

Math, science, and music operate in the context of honesty, openness, and collaboration. Learn how mathematicians and scientists receive recognition for their work. Creativity and imagination lead to questions which can result in new discoveries.

Infinite Precision (03:17)

Infinity is a number greater than the amount of stars in the universe and grains of sand on Earth. Mathematics provides tools to understand the concept of infinity; see examples.

Infinite Precision: Pairing (07:39)

To make a mathematical concept precise, you have to ask, what does it mean? Experts discuss various ways to explore infinity, including cardinality, and how to find a new number.

Computing for Visualization (02:31)

At the National Center for Supercomputing Applications (NSCA), scientific visualization helps experts understand complex areas. Donna Cox draws similarities between artists and scientists.

Computing for Visualization: Supercomputers (04:28)

Many scientists, including Einstein, create visual models. Technological advancement opens new areas to mathematics; Cox developed pseudo color strategy. Supercomputers make scientific visualization possible.

Computing for Visualization: Forecasting (03:22)

Supercomputers can help weather forecasters better understand storms and provide a look at the universe. Cox considers the future of visualization.

Math in Innovation (03:11)

Mathematical codes and equations control ASIMO's movements. Rodney Brooks and students at MIT work to create autonomous robots.

Math in Innovation: Autonomous Robotics (06:27)

Meet Mertz and Domo. Mathematical concepts dictate Mertz's ability to move and learn; Lijin Aryananda explains. Domo was designed to learn hand-eye coordination using geometric and trigonometric principles.

Playing by Rules (05:44)

Designer Jhane Barnes found inspiration for her high-end menswear in the rules of mathematics. She teamed with Bill Jones and Dana Cartwright to design fabrics on her computer. Barnes creates clothing lines inspired by fractals.

Playing by Rules: Mandlebrot Set (03:43)

Buyers look at Barnes' new line of clothing inspired by the Mandelbrot set. The Mandelbrot set is self-similar.

Fractals: A New Geometry? (01:34)

The concept of fractals was not fully explored until the advent of computers. Computers are an integral part of Barnes' design process.

Credits: Discovering Math: Advanced—The General Nature and Uses of Math (00:49)

Credits: Discovering Math: Advanced—The General Nature and Uses of Math