The Controllability Gramian is a mathematical construct used in control theory to assess the controllability of a linear time-invariant (LTI) system. Specifically, it provides a way to determine whether it is possible to drive the state of a dynamical system to any desired condition through appropriate control inputs.

The American Automatic Control Council (AACC) is an organization dedicated to promoting the advancement and application of automatic control systems and technologies. It serves as an umbrella for several professional societies, including the Association for Automatic Control Engineering (AACE), the IEEE Control Systems Society (CSS), the American Society of Mechanical Engineers (ASME), and others. The AACC aims to foster collaboration among these societies to enhance the field of automatic control.

Adaptive control is a type of control strategy used in control systems where the controller parameters can change dynamically in response to variations in the system or environment. Unlike traditional control systems, which typically use fixed parameters, adaptive control systems can adjust their parameters in real-time to maintain optimal performance despite changes in system dynamics or external disturbances.

Stability theory is a branch of mathematics and systems theory that deals with the stability of solutions to dynamic systems, particularly in the context of differential equations and control theory. The central question in stability theory is whether small perturbations or changes in the initial conditions of a system will lead to small changes in its future behavior.

RANDU is a pseudorandom number generator that was developed in the early 1950s at IBM.

Tinkertoy is a classic construction toy that consists of rods and spools (or other connectors) that can be assembled in various ways to create structures, models, and designs. Originally invented by Charles H. Pajeau and his brother-in-law, the toy was first introduced in 1914. The components typically include wooden or plastic rods of various lengths and cylindrical or disk-shaped connectors that allow users to create a wide range of shapes, from simple geometric forms to complex structures.

This is an interesting initiative which has some similarities to Ciro Santilli's OurBigBook project.

The fatal flaw of the initiative in Ciro Santilli's opinion is the lack of user-generated content. We will never get there without UGC and algorithms, never.

Also as of 2021, it mostly useless business courses: learn.saylor.org unfortunately.

But it has several redeeming factors which Ciro Santilli aproves of:

Licensing appears to be a mixed mess between the dreaded CC BY-NC-SA and the good CC BY, e.g.:?

The founder Michael J. Saylor looks a bit crooked, Rich people who create charitable prizes are often crooked comes to mind. But maybe he's just weird.

Toy blocks are simple, often colorful, geometric shapes that are designed primarily for play. They are typically made from wood, plastic, or foam and come in various sizes, shapes, and colors. Toy blocks have been popular among children for generations and are used for a range of activities, including stacking, building, and creative play.

Trix is a toy line primarily targeted at young children, which features a variety of toys, games, and activities designed to encourage imaginative play and creativity. The line often includes items like dolls, vehicles, playsets, and building kits. Trix toys are typically known for their colorful designs and playful themes, making them appealing to kids. The brand has been used in various contexts, but it primarily focuses on providing engaging and entertaining products for children.

Zome is a term that might refer to different things depending on the context, but one prominent use of "Zome" is in relation to Zome Tools, an educational toolset created for learning geometry, mathematics, and the principles of polyhedra and space. Zome Tools are colorful geometric building pieces that can be connected to create various structures, allowing users to explore spatial relationships and mathematical concepts in an engaging and interactive way.

The Axiom Schema of Predicative Separation is a principle in certain foundations of mathematics, particularly in systems that adopt a predicative approach to set theory, like the predicative versions of constructive set theories or in the area of predicative mathematics. In general, the Axiom Schema of Separation is an axiom that allows for the construction of subsets from given sets based on a property defined by a formula.

Bar induction is a mathematical technique used to prove statements about all natural numbers, particularly statements concerning well-ordering and induction principles that extend beyond standard mathematical induction. It applies to structures that have the properties of natural numbers (like well-ordering) but may involve more complex or abstract systems, such as ordinals or certain algebraic structures. The concept is particularly important in set theory and is often used in the context of proving results about various classes of sets or functions.

The Brouwer–Hilbert controversy refers to a fundamental disagreement between two prominent mathematicians, L.E.J. Brouwer and David Hilbert, regarding the foundations of mathematics, specifically concerning the nature of mathematical existence and the interpretation of mathematical entities. **Background:** Brouwer was a proponent of intuitionism, a philosophy that emphasizes the idea that mathematical truths are not discovered but constructed by the human mind.

Schrödinger equation for a one dimensional particle with $V=0$. The first step is to calculate the time-independent Schrödinger equation for a free one dimensional particle

Then, for each energy $E$, from the discussion at Section "Solving the Schrodinger equation with the time-independent Schrödinger equation", the solution is:Therefore, we see that the solution is made up of infinitely many plane wave functions.

A **choice sequence** is a concept primarily utilized in mathematics and particularly in set theory and topology. It refers to a sequence that is constructed by making a choice from a collection of sets or elements at each index of the sequence.

Church's thesis, also known as Church's conjecture or the Church-Turing thesis, is a fundamental concept in computation and mathematical logic. In the context of constructive mathematics, it relates to the limits of what can be effectively computed or decided by algorithms or mechanical processes. In more precise terms, Church's thesis posits that every effectively calculable function (one that can be computed by a mechanical process) is computably equivalent to a recursive function.