Erich Kähler (1917–2010) was a prominent German mathematician known for his contributions to several areas of mathematics, particularly in the fields of differential geometry and complex geometry. He is best known for the Kähler metric, which is a type of Riemannian metric that arises in complex differential geometry. Kähler's work has had significant implications in various areas, including algebraic geometry and mathematical physics.
Erich Sackmann is a notable German physicist recognized for his contributions to the field of biophysics. He has been particularly influential in the study of cell mechanics and the physical properties of biological membranes. Sackmann’s research has included topics such as the dynamics of membrane proteins, the behavior of lipid bilayers, and the mechanical properties of cells. His work has implications for understanding various biological processes and diseases at the microscopic level.
Eric Vanden-Eijnden is a notable figure in the field of applied mathematics and computational science. He is known for his work in areas such as dynamical systems, numerical analysis, and machine learning, particularly in the context of studying complex systems. His research often involves the development of algorithms and techniques for simulating and understanding the behavior of dynamical systems and for applying these methods to practical problems.
Ernest William Brown (1866–1938) was an English mathematician and astronomer known for his work in celestial mechanics and astrodynamics. He contributed significantly to the development of astronomical theories and methods, particularly related to the calculation of planetary orbits. One of his notable achievements was in advancing the analytical techniques for solving the three-body problem and other complex orbital motions.
Ernst Abbe (1840–1905) was a German physicist and optician renowned for his contributions to the field of optics and microscopy. He is best known for his work on the theory of optical imaging and for his inventions that improved the design of microscopes. Abbe formulated the Abbe sine condition, which provides guidelines for the design of high-performance optical systems.
As of my last knowledge update in October 2023, there is no widely recognized individual, organization, or concept known as "Ernst Rexer." It is possible that it could refer to a lesser-known person or a new entity that emerged after that date.
Probabilistic inequalities are mathematical inequalities that involve probabilities and provide bounds on the likelihood of certain events or random variables. These inequalities are useful in probability theory and statistics, as they help in understanding the behavior of random variables, enabling us to make predictions and infer properties of distributions.
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