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.

Optional Writing Activity

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

Gordon Bell is a pioneering computer designer with an influential career in industry, academia and government. He graduated from MIT with a degree in electrical engineering. From 1960, at Digital Equipment Corporation (DEC), he designed the first mini- and time-sharing computers and was responsible for DEC's VAX as Vice President of R&D, with a 6 year sabbatical at Carnegie Mellon University. In 1987, as NSF’s first, Ass't Director for Computing (CISE), he led the National Research Network panel that became the Internet. Bell maintains three interests: computing, lifelogging, and startup companies—advising over 100 companies. He is a Fellow of the, Association of Computing Machinery, Institute of Electrical and Electronic Engineers, and four academies. He received The 1991 National Medal of Technology. He is a founding trustee of the Computer History Museum, Mountain View, CA. and is an Researcher Emeritus at Microsoft. His 3 word descriptor: Computing my life; computing, my life.

Turing machine
Alan Mathison Turing
Alan Mathison Turing

Did you know that computing has been used in military espionage and has even influenced the outcome of major wars? Alan Mathison Turing designed the code breaking machine that enabled the deciphering of German communications during WWII. As per the words of Winston Churchill, this would remain the single largest contribution to victory. In addition, he laid the groundwork for visionary fields such as automatic computing engines, artificial intelligence and morphogenesis. Despite his influential work in the field of computing, Turing experienced extreme prejudice during his lifetime regarding his sexual orientation. There is no doubt that computers are ubiquitously part of our lives due to the infusion of Turing’s contributions.

@ symbol
Ray Tomlinson
Ray Tomlinson

Have you ever considered that someone, at some point, was in a position to choose what symbol would be used separate the user from their location in an email address? That person, it turns out, was Ray Tomlinson, and in 1971 he chose "@". Tomlinson is credited with demonstrating the first email sent between computers on a network, and when asked what inspired him to make this selection he said, “Mostly because it seemed like a neat idea.”

After completing his Master’s degree at MIT in 1965, Ray joined the Information Sciences Division of Bolt Beranek and Newman Inc. of Cambridge, Massachusetts. Since then he has made many notable contributions to the world of network computing. He was a co-developer of the TENEX computer system that was popular in the earliest days of the Internet; he developed the packet radio protocols used in the earliest internetworking experiments; he created the first implementation of TCP; and he was the principle designer of the first workstation attached to the Internet.

CGA palette
Mark Dean

If you have ever used a PC with a color display you have been acquainted with the work of Mark Dean. After achieving a Bachelor’s degree in electrical engineering from the University of Tennessee, Dean began his career at IBM. Dean served as the chief engineer on the team that developed the first IBM PC, for which he currently holds one third of the patents. With colleague Dennis Moeller, he developed the Industry Standard Architecture (ISA) systems bus, which enabled peripheral devices such as printers, keyboards, and modems to be directly connected to computers, making them both affordable and practical. He also developed the Color Graphics Adapter which allowed for color display on the PC. Most recently, Dean spearheaded the team that developed the one-gigahertz processor chip. Dean went on to obtain a MSEE from Florida Atlantic University and a Ph.D. in electrical engineering from Stanford University. He is a member of the National Academy of Engineering, has been inducted into the National Inventors Hall of Fame, and is the first African-American IBM Fellow.

RISC processor
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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