Encouraging truck - rough roads ahead! |
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S. Gill Williamson, Professor Emeritus |
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Research Area: Algorithmic Combinatorics |
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gill.williamson AT gmail.com or gill AT cs.ucsd.edu |
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Astronomy/Botany trip in Kofa |
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Bender-Williamson Online Lecture Series: a free, downloadable two quarter or two semester course in discrete mathematics (pdf files). This material was taught by the authors and other faculty to lower division students in mathematics and computer science at the University of California, San Diego. All exercises and many variations of them have been worked on homework and exams by our students. |
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Foundations of Combinatorics with Applications: This upper division or beginning graduate course in combinatorics is broken down into basic units in order to make it more flexible as a supplementary text or reference. Numerous exercises with a solutions manual are provided. All files are free, downloadable pdf files. A link to the Dover edition that contains all of this material is provided. |
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Seminar in algorithmic combinatorics: This beginning graduate level seminar studies the use of geometric and algebraic structures to compare and classify combinatorial algorithms. The geometric concepts, in particular, are useful in both complexity analysis and practical programming. Topics are in small units that are downloadable pdf files. Choose those that relate to your interests. |
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A Comprehensive Introduction to Linear Algebra, Broida and Williamson, Addison Wesley 1989, is a book written for upper division undergraduates in mathematics and related fields. We have taken the original MS Word legacy pdf chapter files and converted them to Adobe Acrobat pdf files optimized for web viewing and downloading. This material has been designated Creative Commons (CC0,1.0) to allow flexibility of use, including conversion to modern mathematical typesetting standards (e.g., LaTeX) by anyone interested in doing so. |
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Top-down Calculus - a concise course: This one-quarter or one-semester calculus course was designed as a part of a UCSD summer program to give high school math teachers extra training in calculus. Key ideas are developed and put to use quickly (e.g., the chain-rule on page 11). This text has been used successfully for UCSD summer school students. All material is free, downlable pdf files. |
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Anacardiaceae - Sumac Plant Family: As a docent volunteer at our local park, Torrey Pines SNR, I am charged with explaining the park's natural history. I have prepared this brief training site to introduce visitors to the most evident botanical traits of one of our important plant families. Roll the cursor over the gray, green and red rectangles, click on the yellow. Print the field notes to take on hikes. |
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Geology Manifold: For various state and national parks, pdf charts with links to local geological information are given. Geological time intervals where formations are present in the region are indicated by red hyperlinks (e.g. Eocene). Other time intervals ("missing geology") are represented by black hyperlinks (e.g., Miocene). Links are to Wikipedia, Palaeos, or local sites. |
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"Synthetic intelligence" in our discussion refers to civilizations of highly intelligent robots that are artifacts of biologically evolved technological civilizations. I have written some fiction: The Avatars Remember Nothing (short story) and The Observers (short novel) on this subject. For a discussion of synthetic intelligence as it relates to SETI see the referenced articles by Seth Shostak. |
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Assertion: "The cosmological multiverse has interesting properties that are provably unprovable (true or false) using theoretical physics." Lacking a precise description of the multiverse, we can't prove this assertion. We can define analogous "lattice multiverses" with such properties, suggesting (not proving) that multiverses now being proposed by physicists may have such unprovable properties also. |
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Research: A sample of my research interests is here. Items 1, 2, 4 and 6 involve group theory and combinatorics. Items 5, 8, 14 and 15 concern efficient listing algorithms. Item 10 is asymptotic analysis. Items 12 and 13 concern sorting networks. Recent research (click here) concerns ranking and random generation of combinatorial objects. Math geneaology is here. Education: Santa Barbara High School 1953-56; Caltech 1956-60, BS Math; Stanford 1960-62, MS Statistics; Univ. Calif. Santa Barbara 1962-65, Ph.D. Mathematics. Professional: UCSD, Professor of Mathematics 1965-91; UCSD, Professor Computer Science and Engineering 1991-2004 (retired). |
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