## Jim Herod's Lectures on Hilbert Spaces for Science...

by: Maple
MaplePrimes own Jim Herod has a wonderful set of lecture notes—accompanied by a collection of Maple worksheets—which introduce linear operators on infinite-dimensional Hilbert spaces to beginning graduate students in science and engineering. Entitled Linear Algebra, Infinite Dimensions, and Maple, these notes were developed from a one quarter course which Prof. Herod taught many times at the Georgia Institute of Technology. The notes are very concise and have been refined and improved many times over the years in response to student feedback.

## Knots

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Take a piece of string — I mean literally, go get a piece of string and tie it into a knot. Now tape the two ends together so it makes a closed loop — necessary to fulfill the mathematical definition of a "knot." How many different knot types do you think there are? The number is infinite, and the question of how to categorize these manifestations of loopiness has engaged some of the finest mathematical minds for a century. Original story

## Math/CS Career Advice & Job Listings

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Now that you have a shiny new degree in mathematics or computer science, how do you get a job in your field? There are many online resources which can help you succeed in your quest!

## Maplets for Calculus

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Maplets for Calculus is a collection of maplets designed to help students practice their calculus problem-solving skills and to assist instructors in providing effective classroom demonstrations (including 2- and 3-D visualization -- even animation). The maplets cover all major topics in single-variable calculus - limits, derivatives, integrals, differential equations, sequences, series, and polar coordinates. Some of the maplets help to build intuition and some provide practice with routine computational techniques. An individual license for Maplets for Calculus is available through the MapleConnect program at . Lab/Classroom bundles and site licenses are also available. The complete list of maplets and sample videos may be seen at .

## First steps in percolation

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I put on PhiMaTeX a simple sheet implementing first steps in percolation simulation : Percolation

## The Math Rap

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Here is a nice video that "might" be helpful to students learning about Pi. It is a rap music video created by a public television station in Boston. It has to be seen to be believed, and it is quite funny.

## BinaryArithmetic package

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I was getting bored of having to convert between binary and decimal to find examples for binary arithmetc, so I decided to write a package which automatically interprets all input numeric values as binary numbers, makes the appropriate calculation (by converting back to decimal, doing the operation and then converting back to binary.

## Solving a Sudoku Puzzle with Maple

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During my stay in Los Angeles last week, I visited a nephew of mine and noticed that he had solved several of the Sudoku puzzles that appear daily in the LA Times. Not interested in solving a particular problem, I instead thought about how to solve this generally in Maple. Here is a pdf describing my solution and a maple file that implements it. I slightly generalized the problem, allowing any m×m grid.

## Continuing the Textbook Discussion

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Thanks for the considered words from Tom, Jim and Trogdor The Burninator, the origins of the name lost in the mists of time?! Tom mentioned several points that I'd like to comment on. The use of extra study books, written at a lower level, is a strategy that I see some local students use. Interstingly though its the more successful student who is using them. The student whom I encounter usually doesn't do this. They have the official text and maybe some printed lecture notes from the internet and thats it. I suspect in this case the problem isn't just the math but the concept of how to study math that is the problem.

## Seeking Opinions on Calculus Textbooks and Content...

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I suppose I'll jump in to the world of the blog with a question: What do you consider to be a solid and accessible introductory textbook to calculus? By Solid I mean: No gaps in coverage that leave the reader at a disadvantage because of unclear text and examples or outright missed topics. By Accessible I mean: Written so the average student can expect to understand the concepts directly or with a small amount of help outside the classroom.

## Non-differentiable functions...

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There are some "interesting" functions which I learned about in undergrad: the Weierstrass function is differentiable nowhere, and the 'Christmas-tree' function is continuous at the irrationals and not differentiable at the rationals.

## Two Illustrations of "Is g the same as f?"

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Here are two illustrations for how one might want to check to see if g is the same as f. The attached file is a Maple 10 worksheet.

## Series and Tests for Their Convergence

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A question was asked in the forums about series tests. I saw that this would also make an excellent weblog entry as well. In answer to the questions: How can I get Maple to determine if a series converges or diverges? and How can I obtain the general representation of a formal power series for a function? I offer the following advice:

## Dumb Kopf...

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I hadn't carefully read the puzzle conditions of the Kopf und Kopf puzzle mentioned by Thomas Richard, I didn't realize that the digits had to be unique. He asked for a hint on how to handle that with my recursive method. The idea is simple, add a parameter (to the recursive procedure) that supplies the available digits. I've attached the code that does this. This would have been a response, rather than a separate blog entry, however, there does not appear to be a way to add attachments to a response.
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