James Mercer is a mathematician best known for his contributions to functional analysis and statistics, particularly in the development of the Mercer theorem. The Mercer theorem provides conditions under which a continuous positive semidefinite kernel can be represented in terms of an infinite series of eigenfunctions. This has important applications in various fields, including machine learning, where it is often used in the context of support vector machines and kernel methods.
John Edensor Littlewood (1885–1977) was an influential English mathematician known for his contributions to various areas of mathematics, particularly in analysis, number theory, and mathematical logic. He is well-remembered for his collaboration with G.H. Hardy, with whom he co-authored several important works, including the famous "Hardy-Littlewood Method," which involves techniques in analytic number theory.
John Horvath is a mathematician known for his contributions to various areas of mathematics, including functional analysis, partial differential equations, and mathematical logic. His work often involves applied mathematics and theoretical research. Specific details about his birth, education, and major works may not be widely published, but he may be recognized in academic circles for specific contributions to mathematical theory and practice. For more in-depth information about his research and publications, it's best to consult academic databases or his professional profiles on institutional websites.
Jonathan Partington is a mathematician known for his work in the field of mathematics, particularly in analysis and topology. He is also recognized for his contributions to the educational aspect of mathematics, often sharing his insights through lectures, publications, and online resources.
Joseph L. Doob (1910–2004) was an influential American mathematician known primarily for his contributions to the fields of probability theory and stochastic processes. He is renowned for his work on measure theory and for developing concepts that laid the groundwork for modern probability. Among his significant contributions is the formulation of Doob's martingale concept, which has extensive applications in various areas, including financial mathematics, statistics, and mathematical physics.
Pinned article: 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 3. Visual Studio Code extension installation.Figure 4. Visual Studio Code extension tree navigation.Figure 5. Web editor. 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.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - 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





