Coloring Discrete Structures

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Lesson synopsis

coloring conceptIs it true or false that Discrete Structures and Discrete Mathematics are the same thing? This is the kind of question that is asked in this field – or both fields if they are indeed different. Most Middle School students see a mix of discrete and continuous math without ever noticing the difference. This lesson introduces them to areas of mathematics that computer scientists use to do computational problems. Search techniques through discrete structures are illustrated through graph traversal and graph coloring.

Age Levels

11 - 13 years

Objectives

Introduce students to:
the relationship between Discrete Structures and Discrete Mathematics.
the difference between discrete and continuous phenomenon.
how to answer a question with sets.
how a discrete problem is solved through search: specifically graph coloring.

Anticipated learner outcomes

Students will be able to:
explain the difference between continuous and discrete structures.
discuss the difference in perspective of discrete math and discrete structures.
form a problem statement as a logical proposition, a Venn diagram, and an adjacency graph.
color a map with the least number of colors.

Internet Connections

Continuous vs. Discrete
https://youtu.be/WX0hnuniLpI
Map Coloring
https://youtu.be/ANY7X-_wpNs

Recommended Reading

http://wiki.acm.org/cs2001/index.php?title=Discrete_structures
http://www.cse.buffalo.edu/~rapaport/191/S09/whatisdiscmath.html
http://www.purplemath.com/modules/venndiag4.htm
https://en.wikipedia.org/wiki/Set_(mathematics)
https://en.wikipedia.org/wiki/Intersection_(set_theory)

Optional Writing Activity

Is it true or false that Discrete Structures and Discrete Mathematics are the same thing? Defend your answer.

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John Hennessy
John Hennessy

Have you ever wondered how computers can execute complex commands in mere seconds? John Hennessy is a pioneer of reduced instruction set computing (RISC) architecture which employs small, highly-optimized sets of instructions to greatly enhance computer performance. He was instrumental in transferring the technology, specifically MIPS RISC architecture, to industry. He co-founded MIPS Technologies and co-authored the classic textbook with David A. Patterson, on Computer Architecture.

As Stanford faculty he rose to be the Chairman of the Computer Science Department, Dean of the School of Engineering, then Provost and finally the President of Stanford in 2000 (and till date). Hennessy holds a Master’s and Ph.D. in Computer Science from SUNY Stony Brook. He is an IEEE Fellow and was selected to receive the IEEE Medal of Honor in 2012. Hennessey also launched significant activities that helped to foster interdisciplinary research in the biosciences and bioengineering at Stanford.

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James Dammann

If you have used a word processor today, moved your mouse on your laptop, dragged an object around on your smartphone, or highlighted a section of text on your tablet, you can thank Jim Dammann. In 1961 during his second year at IBM and just one year after completing his PhD, Jim created the concept of what today we all take for granted -- the cursor. This idea he documented in utilizing the cursor within word processing operations.

After retiring from IBM, Jim went on to inspire future generations of software engineers at Florida Atlantic University. His work there too demonstrated his creativity for he spent considerable effort enhancing their software engineering program by integrating ideas and feedback from local industries into the University curricular. Today, Jim lives in the Westlake Hills west of Austin Texas and spends most of his time in his art studio. He wrote and published The Opaque Decanter, a collection of poems about art, which provided a new view at part of art history.

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Jean Sammet

Jean E. Sammet was one of the first developers and researchers in programming languages. During the 1950’s - 1960’s she supervised the first scientific programming group for Sperry Gyroscope Co. and served as a key member of the original COBOL (COmmon Business-Oriented Language) committee at Sylvania Electric Products. She also taught one of the first graduate programming courses in the country at Adelphi College. After joining IBM in 1961, she developed and directed the first FORMAC (FORmula MAnipulation Compiler). This was the first widely used general language and system for manipulating nonnumeric algebraic expressions. In 1979 she began handling Ada activities for IBM’s Federal Systems Division. Ada is a structured, object-oriented high-level computer programming language, designed for large, long-lived applications, where reliability and efficiency are paramount. Jean has a B.A. from Mount Holyoke College and an M.A. from the University of Illinois, both in Mathematics. She received an honorary D.Sc. from Mount Holyoke (1978).

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Cleve Moler

Cleve Moler improved the quality and accessibility of mathematical software and created a highly respected software system called MATLAB. He was a professor of mathematics and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. In the late 1970’s to early 1980’s he developed several mathematical software packages to support computational science and engineering. These packages eventually formed the basis of MATLAB, a programming environment for algorithm development, data analysis, visualization, and numerical computation. MATLAB can be used to solve technical computing problems faster than with traditional programming languages, such as C, C++, and Fortran. Today, Professor Moler spends his time writing books, articles, and MATLAB programs.

Listen to what Professor Moler has to say about his life’s work: http://www.youtube.com/watch?v=IT5umwNSAxE

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Liz Gerber - Image credit Lisa Beth Anderson
Liz Gerber
Liz Gerber - Image credit Lisa Beth Anderson

Liz Gerber earned her MS and PhD in Product Design and Management Science and Engineering at Stanford. She specializes in design and human-computer interaction, particularly how social computing supports the innovation process. Her current research investigates crowd-funding as a mechanism for reducing disparities in entrepreneurship.
Gerber's work funded by the US National Science Foundation and the National Collegiate Inventors and Innovators Alliance has appeared in peer-reviewed journals, including Transactions on Computer Human Interactions, Design Studies, and Organization Science.
As an award-winning teacher and researcher, Liz has touched the lives of more than 6,000 students through her teaching at Northwestern's Segal Design Institute and Stanford University's Hasso Plattner's Institute of Design and through her paradigm-shifting creation, Design for America, a national network of students using design to tackle social challenges.

Image credit - Lisa Beth Anderson

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