We define this as the functional equation:It is a bit like cauchy's functional equation but with multiplication instead of addition.

So that he can work full time on OurBigBook.com and revolutionize advanced university-level science, technology, engineering, and mathematics eduction for all ages.

Donating to Ciro is the most effective donation per dollar that you can make to:

Ciro's goal in life is to help kids as young as possible to reach, and the push, the frontiers of natural sciences human knowledge, linking it to applications that might be the the next big thing as early as possible. Because nothing is more motivating to students than that feeling of:rather than repeating the same crap that everyone is already learning.

To do this, Ciro wants to work in parallel both on:

Ciro believes that this rare combination of both:produces a virtuous circle, because Ciro:

As explained at OurBigBook.com and high flying bird scientist, Ciro is most excited to make contributions at the "missing middle level of specialization" that lies around later undergrad and lower grad education:But on that middle sweet spot, Ciro believes that something can be done, in such as way that delivers:in a way that is:

Ciro believes that today's society just keep saying over and over: "STEM is good", "STEM is good", "STEM is good" as a religious mantra, but fails miserably at providing free learning material and interaction opportunities for people to actually learn it at a deep enough level to truly appreciate why "STEM is good". This is what he wants to fix.

The following quote is ripped from Gwern Branwen's Patreon page, and it perfectly synthesizes how Ciro feels as well:

In addition to all of this, financial support also helps Ciro continue his general community support activities:

Good list: en.wikipedia.org/wiki/Geologic_time_scale#Terminology

Anna Barbara Reinhart does not appear to be a widely recognized name in historical or popular contexts as of my last training cut-off in October 2023. It could be a name associated with a lesser-known individual, fictional character, or a specific context not covered in common sources.

Albert Pfluger is not widely known in the public domain as of my last update in October 2023, and there may be multiple individuals with that name.

Giorgio Margaritondo is a notable figure in the fields of physics and materials science, particularly recognized for his contributions to synchrotron radiation research and nanotechnology. He has held academic positions and has been involved in various research projects and collaborations related to the application of synchrotron light in studying materials and biological systems. Margaritondo is also known for his work in promoting the use of advanced techniques in scientific research, and he has published numerous articles related to his research interests.

Heinrich Rohrer was a Swiss physicist, notable for his contributions to the field of nanotechnology and surface science. He is best known for his work on the development of the scanning tunneling microscope (STM) alongside Gerd Binnig. The STM, which was developed in the early 1980s, allows researchers to image and manipulate individual atoms on surfaces, significantly advancing the field of nanotechnology and allowing for the exploration of materials at the atomic scale.

In mathematics, particularly in the field of group theory, a group action is a way in which a group can operate on a mathematical object. More formally, if \( G \) is a group and \( X \) is a set, a group action of \( G \) on \( X \) is a function that describes how elements of the group transform elements of the set.

CPT symmetry is a fundamental principle in theoretical physics that combines three symmetries: Charge conjugation (C), Parity transformation (P), and Time reversal (T). 1. **Charge Conjugation (C)**: This symmetry relates particles to their antiparticles. For example, it transforms an electron into a positron and vice versa. 2. **Parity Transformation (P)**: This symmetry involves flipping the spatial coordinates, effectively reflecting a system through the origin.

Coxeter notation is a way of representing regular polytopes and their higher-dimensional analogs (such as regular polygons, polyhedra, and polychora) using a system based on pairs of numbers. It employs a compact notation that often consists of a string of integers, occasionally including letters or specific symbols to indicate certain geometric properties, relations, or symmetries.

A crystallographic point group is a mathematical classification of the symmetry of a crystal structure. These groups describe the symmetry operations that leave at least one point (typically the origin) invariant, meaning those operations do not alter the position of that point. The main symmetry operations included in crystallographic point groups are: 1. **Rotation**: Turning the crystal around an axis. 2. **Reflection**: Flipping the crystal across a plane.

The FKG inequality, named after its contributors Fortuin, Kasteleyn, and Ginibre, is a result in probability theory that provides a relationship among joint distributions of certain random variables, particularly in the context of lattice structures, such as spins in statistical mechanics. It is most commonly applied in the study of lattice models in statistical physics, including the Ising model.

Inversion transformation typically refers to an operation used in various fields, including mathematics, computer science, statistics, and image processing. The specific meaning can vary based on the context, but here are a few common interpretations: 1. **Mathematics**: In mathematics, an inversion transformation often refers to a transformation that maps points in a space such that points are inverted relative to a particular point (the center of inversion) or a shape (like a circle or sphere).

A **non-Euclidean crystallographic group** refers to a symmetry group that arises in the study of lattices and patterns in geometries that are not based on Euclidean space. Crystallographic groups describe how a pattern can be repeated in space while maintaining certain symmetries, including rotations, translations, and reflections. In Euclidean geometry, the classifications of crystallographic groups are based on the 17 two-dimensional plane groups and the 230 three-dimensional space groups.

Supersymmetry (SUSY) is a theoretical framework in particle physics that proposes a symmetry between two basic classes of particles: fermions (which make up matter, like electrons and quarks) and bosons (which mediate forces, like photons and gluons). In a fully realized supersymmetric model, each particle in the Standard Model of particle physics would have a superpartner with differing spin.

Isoelastic utility, also known as constant relative risk aversion (CRRA) utility, is a type of utility function used in economics to model the preferences of individuals with respect to consumption over time and uncertainty. The key characteristics of isoelastic utility are that it represents a consistent level of relative risk aversion and exhibits constant elasticity of substitution between different levels of consumption.

In grammar, an antecedent is the word, phrase, or clause that a pronoun refers to or replaces. It typically appears earlier in the sentence or in a preceding sentence. Understanding the relationship between an antecedent and its pronoun is crucial for clarity and coherence in writing. For example, in the sentence: "The dog barked loudly, and it scared the neighbors." Here, "the dog" is the antecedent of the pronoun "it.

A verbless clause is a clause that does not contain a verb. In English, these clauses can take various forms but typically rely on the use of nouns, adjectives, and other parts of speech to convey meaning. Verbless clauses often provide additional information, describe a condition, or state an action in a more concise way. Here are a few examples of verbless clauses: 1. **Noun phrases**: "Her smile, a ray of sunshine, brightened the room.

Sloppy identity refers to a phenomenon in linguistics and philosophy of language, particularly in the context of ellipsis and identity statements. It describes scenarios where the identity condition between expressions can become "sloppy" or less strict due to the presence of ellipsis or context-specific interpretations. For example, in sentences involving ellipsis, like: - "Sam loves pizza, and so does Alex.

Darmstadtium is a synthetic chemical element with the symbol Ds and atomic number 110. It was first synthesized in 1994 by a team of German scientists at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany, from which it takes its name. Darmstadtium is a member of the transition metals on the periodic table and is classified as a superheavy element.