Dennis Shasha is an American computer scientist, known for his work in the fields of database systems, data mining, and computer security. He is also a professor at New York University's Tandon School of Engineering. In addition to his academic contributions, Shasha has written several books that bridge the gap between technology and various aspects of culture. One of his notable works is "The Art of Data Science," where he explores the intersection of data analysis and creativity.
Douglas Hofstadter is an American cognitive scientist, author, and philosopher, best known for his work in the fields of artificial intelligence, cognitive science, and the philosophy of mind. He gained widespread recognition for his book "Gödel, Escher, Bach: An Eternal Golden Braid," published in 1979, which explores the relationships between the works of mathematician Kurt Gödel, artist M.C. Escher, and composer J.S. Bach.
Ed Pegg Jr. is a mathematician known for his work in recreational mathematics, particularly in areas such as number theory and mathematical puzzles. He is also recognized for his contributions to the online mathematics community, including various publications and problem-solving resources. Pegg is one of the contributors to the website "Wolfram MathWorld" and has worked for Wolfram Research, the company behind Mathematica.
Henry Dudeney (1857-1930) was an English mathematician and puzzle creator, known for his contributions to recreational mathematics. He is particularly famous for his work in logic puzzles, geometric puzzles, and mathematical games.
Henry Segerman is a mathematician and educator known for his work in mathematics, particularly in geometry and topology. He is also recognized for his efforts to promote mathematical visualization and accessibility through various mediums, including 3D printing and educational outreach. Segerman has contributed to the field by creating mathematical art and models, which help illustrate complex concepts in an engaging way.
Ivan Moscovich is a notable inventor, puzzle creator, and author, known for his work in the field of educational toys and games. He has designed numerous puzzles and has contributed to the development of innovative educational materials that engage children's problem-solving skills and foster creativity. Moscovich has also been recognized for his contributions to the field of mathematics and logic through his various publications and inventions. In addition to his work as a puzzle designer, he has been involved in the promotion of scientific and mathematical education.
A quantum well is a potential energy structure where charge carriers (such as electrons and holes) are confined in a very thin region, typically on the nanometer scale. This confinement occurs in one dimension, allowing the carriers to move freely in the other two dimensions. Quantum wells are a key component in various semiconductor devices and have a significant impact on their electronic and optical properties.
A knot polynomial is a mathematical invariant associated with knots and links in the field of knot theory, which is a branch of topology. Knot polynomials are used to distinguish between different knots and to study their properties. Some of the most well-known knot polynomials include: 1. **Alexander Polynomial**: This is one of the earliest knot polynomials, defined for a knot or link as a polynomial in one variable. It provides insights into the topology of the knot and can help distinguish between different knots.
A Laurent polynomial is a type of polynomial that allows for both positive and negative integer powers of the variable.
Polynomial matrix spectral factorization is a mathematical technique used to decompose a polynomial matrix into a specific form, often relating to systems theory, control theory, and signal processing. The basic idea is to express a given polynomial matrix as a product of simpler matrices, typically involving a spectral factor that reveals more information about the original polynomial matrix. ### Key Concepts 1. **Polynomial Matrix**: A polynomial matrix is a matrix whose entries are polynomials in one or more variables.
Mittag-Leffler polynomials are a class of special functions that arise in the context of complex analysis and approximation theory. They are named after the Swedish mathematician Gösta Mittag-Leffler, who made significant contributions to the field of mathematical analysis.
A **monic polynomial** is a type of polynomial in which the leading coefficient (the coefficient of the term with the highest degree) is equal to 1. For example, the polynomial \[ p(x) = x^3 - 2x^2 + 4x - 5 \] is a monic polynomial because the coefficient of the \( x^3 \) term is 1.
The Morley-Wang-Xu element is a type of finite element used in numerical methods for solving partial differential equations. It is specifically designed for approximating solutions to problems in solid mechanics, particularly those involving bending plates. The element is notable for its use in the context of shallow shells and thin plate problems. It is an extension of the Morley element, which is a triangular finite element primarily used for plate bending problems.
A multilinear polynomial is a polynomial that is linear in each of its variables when all other variables are held constant.
Neville's algorithm is a numerical method used for polynomial interpolation that allows you to compute the value of a polynomial at a specific point based on known values at various points. It is particularly useful because it enables the construction of the interpolating polynomial incrementally, offering a systematic way to refine the approximation as new points are added. The basic idea behind Neville's algorithm is to build a table of divided differences that represent the polynomial interpolation step-by-step.
A P-recursive equation (also known as a polynomially recursive equation) is a type of recurrence relation that can be defined by polynomial expressions.
The Polynomial Wigner–Ville Distribution (PWVD) is an extension of the classical Wigner–Ville distribution (WVD), a time-frequency representation used in signal processing. The WVD offers a method to analyze the energy distribution of a signal over time and frequency, providing insight into its time-varying spectral properties. However, the classical WVD can produce artifacts known as "cross-term interference" when dealing with multi-component signals.
Polynomial evaluation refers to the process of calculating the value of a polynomial expression for a given input (usually a numerical value). A polynomial is a mathematical expression consisting of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
Intro to OurBigBook
. Source. We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivativeVideo 2. OurBigBook Web topics demo. Source. - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.Figure 3. Visual Studio Code extension installation.Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension. - Infinitely deep tables of contents:
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact