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.

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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

King's Quest
Roberta Williams

Video games immerse users in a world of high tech thrills, stunning visuals, unique challenges, and interactivity. They enable users to become a warrior princess or a gruesome ghoul, create a virtual persona, or even develop worlds that other gamers can play on. But before the games of today became reality, they were the dreams of a few innovative individuals.

Roberta Williams is considered one of the pioneers of gaming as we know it today. During the 80’s and 90’s along with husband Ken Williams through their company On-Line Systems, she developed some of the first graphical adventure games. These included such titles as Mystery House, Wizard and the Princess and the popular King’s Quest series. Williams also helped introduce more girls and women to the world of gaming by bringing games developed from a woman’s perspective to mainstream market.

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.

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.

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.

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