Educational Media Reviews Online

Mathematics Illuminated is an engaging and exciting overview of thirteen major concept areas in mathematics. It consists of thirteen 30-minute videos on four DVDs, a book of activities, a facilitator guide for the activities, and a text for participants. A DVD and print set is available for purchase. All materials are freely available on the course web site with streaming video and PDFs. The entire project was created by Annenberg Learner, funded by the Annenberg Foundation, whose primary mission is "encouraging the development of more effective ways to share ideas and knowledge." Mathematics Illuminated was created "for adult learners and high school teachers." The host for the series is Dr. Dan Rockmore, chair of the Mathematics Department and John G. Kemeny Parents Professor of Mathematics at Dartmouth College. Each half hour episode has subsections In the Office, Guest Mathematician, and Real World Connection. Topic 10, Harmonious Math is missing the DVD menu item for In the Office on the review copy. In the Office begins with the host introducing the topic, with historical context showing how concepts have changed over time, building up to today's understanding. The background includes historical and modern-day dramatizations and animations. The Guest Mathematician segment features an expert in dialogue with the host, explaining their work. These guests are drawn from schools like Lewis & Clark College, the University of California at Davis, New York University, and Cornell University. Most presenters are young and enthusiastic mathematicians and physicists. In Real World Connection, other experts appear, discussing their work with concrete examples and applications. Real, tangible examples are often used, e.g., crochet and dice.

The series covers prime numbers, combinatorics, infinity, topology, higher dimensions, symmetry, randomness, non-Euclidean geometries, game theory, the math of harmony, network theory, synchronization and chaos theory. Some lessons build on others, e.g. How Big Is Infinity builds on Combinatorics Counts. Along the way, you'll encounter Pascal's triangle, the traveling salesman and prisoners' problems, the Poincare conjecture, the shape of the universe, Fourier analysis, and social and food networks. Examples are drawn from art, medicine, space flight, cosmology, and biology.

The level of explanation requires basic arithmetic, algebra and geometry, though some discussions are simply conceptual. Instead of focusing entirely on calculations and equations, the videos primarily appeal to the sense of wonder and excitement. One hears words like "beauty," "richness," and "deep." The accompanying text does include more detail, assuming knowledge of algebra, geometry, analytic geometry and differential equations. The videos by themselves provide the least technical introduction to the topic and can be used alone. The activities are designed to be carried out in groups with a facilitator.

The online video includes closed captioning, which is available on the DVDs but only newer players can read them. There are nine interactive activities, only available on the web site. The text covers more detail and material not in the videos and includes a bibliography for further reading. A weakness for teachers is that there is no discussion of teaching these concepts or how they might fit into a curriculum. Advanced placement high school students can learn from this series, and individual programs might work well in an undergraduate mathematics course. Any adult who has completed high school and has a curiosity about mathematics in the modern world will find satisfaction in this well executed series.