###### Physics

- Concepts of Mathematical Physics in Chemistry: A Tribute to Frank E. Harris - Part B, presents a series of articles concerning important topics in quantum chemistry, including surveys of current topics in this rapidly-developing field that has emerged at the cross section of the historically established areas of mathematics, physics, chemistry, and biology. (elsevier.com)
- Categories now appear in many branches of mathematics, some areas of theoretical computer science where they can correspond to types or to database schemas, and mathematical physics where they can be used to describe vector spaces. (wikipedia.org)

###### Geometry

- Introduces elementary logic and mathematical proof using traditional geometry concepts. (lowercolumbia.edu)
- Curvature refers to mathematical concepts in different areas of geometry. (wikipedia.org)
- As such, they are mathematical in that they refer to geometry and arithmetic. (wikipedia.org)

###### Mathematics

- Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. (saxo.com)
- His research interests are theoretical organic chemistry, physical chemistry, mathematical chemistry, graph theory, spectral graph theory and discrete mathematics. (wikipedia.org)
- In mathematics he introduced the notion of graph energy, a concept originating from theoretical chemistry. (wikipedia.org)
- At Texas, Wilder discovered pure mathematics and topology, thanks to the remarkable influence of Robert Lee Moore, the founder of topology in the USA and the inventor of the Moore method for teaching mathematical proof. (wikipedia.org)

###### 1995

- Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought is a 1995 book by Douglas Hofstadter and other members of the Fluid Analogies Research Group exploring the mechanisms of intelligence through computer modeling. (wikipedia.org)
- On April 3, 1995, Fluid Concepts and Creative Analogies became the first book ordered online by an Amazon.com customer. (wikipedia.org)

###### Chemistry

- Other memberships include membership in the International Academy of Mathematical Chemistry, the Academy of Nonlinear Sciences (Moscow) and Academia Europaea. (wikipedia.org)
- Mathematical Concepts in Organic Chemistry. (wikipedia.org)

###### Wilder

- Wilder was vice president of the American Mathematical Society, 1950-1951, president 1955-1956, and the Society's Josiah Willard Gibbs Lecturer in 1969. (wikipedia.org)

###### arithmetic

- As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children's developing competencies with whole-number arithmetic, fractions, and rational numbers. (saxo.com)

###### mechanics

- This important book presents the development, within the framework of continuum mechanics, of the mathematical theory of such accretive forces. (booktopia.com.au)
- S. Gustafson & I.M. Sigal, Mathematical concepts of quantum mechanics. (uni-bonn.de)
- G. Teschl, Mathematical methods in quantum mechanics: With applications to Schrödinger operators. (uni-bonn.de)

###### robot

- Star worlds are mathematical concepts used in robot navigation. (wikipedia.org)

###### significance

- With the increasing tendency in the modern world to place critical importance on many things that simply do not exist, it is hoped that the above initiatives and mathematical techniques can allow people to continue to enjoy placing irrational significance on NEAMCs without inconvenience or harm. (glossynews.com)

###### abstract concepts

- The desire by tourists to be photographed in the vicinity of mathematically useful, although non-existent, abstract concepts has not been confined to Greenwich. (glossynews.com)
- There are, however, many applications where much more abstract concepts are represented by objects and morphisms. (wikipedia.org)

###### American Mathema

- American Mathematical Society. (wikipedia.org)

###### study

- The study illustrates the complexity of learning the symbolic relationships embedded in language, including seemingly simple numerical concepts. (scitech-news.com)
- Objectives: The objective of this study is to build a mathematical model for the existing DMFT index and compare its parameters by suggested new mathematical model. (duhnnae.com)
- Samuel Eilenberg and Saunders Mac Lane introduced the concepts of categories, functors, and natural transformations in 1942-45 in their study of algebraic topology, with the goal of understanding the processes that preserve mathematical structure. (wikipedia.org)
- The study of categories is an attempt to axiomatically capture what is commonly found in various classes of related mathematical structures by relating them to the structure-preserving functions between them. (wikipedia.org)
- A systematic study of category theory then allows us to prove general results about any of these types of mathematical structures from the axioms of a category. (wikipedia.org)
- A similar type of investigation occurs in many mathematical theories, such as the study of continuous maps (morphisms) between topological spaces in topology (the associated category is called Top), and the study of smooth functions (morphisms) in manifold theory. (wikipedia.org)

###### objective

- the learning objective is real-world application of mathematical concepts. (wikipedia.org)

###### basic

- Explores basic visual arts concepts such as the elements of art and the principles of design while engaging students in hands-on creative projects. (lowercolumbia.edu)
- This core vocabulary was designed to encompass concepts common to every human language (such as personal pronouns, body parts, heavenly bodies, verbs of basic actions, numerals 'one' and 'two', etc.), eliminating concepts that are specific to a particular culture or time. (wikipedia.org)
- Any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category-and all the results of category theory apply to it. (wikipedia.org)
- Instead he devised a simplified version of the problem, called SeekWhence, where sequences are based on very simple basic rules not requiring advanced mathematical knowledge. (wikipedia.org)
- Categories, or a priori concepts, have, according to Kant, a basic and necessary importance for human knowledge, even though they are totally different from sensations. (wikipedia.org)

###### form

- The relationships between concepts and the physical world form a substantial part of the subject matter of modern analytical philosophy. (wikisource.org)
- The program is modeled on Jumbo and Copycat and uses a permanent network of known mathematical facts, a working memory in the form of a cytoplasm, and a coderack containing codelets to produce free associations of bricks in order to arrive at the result. (wikipedia.org)
- from Greek: σχῆμα, "form, shape, figure") is the procedural rule by which a category or pure, non-empirical concept is associated with a sense impression. (wikipedia.org)

###### Association

- He was president of the Mathematical Association of America, 1965-1966, which awarded him its Distinguished Service Medal in 1973. (wikipedia.org)
- Mathematical Association of America. (wikipedia.org)

###### graph

- Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms). (wikipedia.org)

###### students

- The term was coined in the United States to describe an approach originally developed in Singapore to teach students to learn and master fewer mathematical concepts at greater detail as well as having them learn these concepts using a three-step learning process: concrete, pictorial, and abstract. (wikipedia.org)
- Students then solve mathematical problems in an abstract way by using numbers and symbols. (wikipedia.org)

###### people

- Concerns have been raised, however, that the importance placed by many people on some "non-existent, abstract mathematical concepts", or NEAMCs, can have a negative psychological impact. (glossynews.com)

###### Several

- Several mathematical concepts can be treated as comma categories. (wikipedia.org)
- An empirical concept is the abstract thought of that which is common to several perceptions. (wikipedia.org)

###### language

- The work may help researchers learn more about how language shapes the way children learn early mathematical concepts, and how that crucial process can go awry in the preschool years. (scitech-news.com)
- The concept of language change is old, and its history is reviewed in Hymes (1973) and Wells (1973). (wikipedia.org)
- The language of category theory has been used to formalize concepts of other high-level abstractions such as sets, rings, and groups. (wikipedia.org)

###### list

- This list contains mathematical concepts named after geographic locations. (wikipedia.org)

###### types

- There are three types of concept that require a schema in order to connect them to perceptions so that they have sense [Sinn] and meaning [Bedeutung]. (wikipedia.org)
- These three types are (1) empirical concepts, (2) pure (mathematical) sensuous concepts, and (3) pure concepts of the understanding, or Categories. (wikipedia.org)

###### theory

- Hence category theory uses abstraction to make it possible to state and prove many intricate and subtle mathematical results in these fields in a much simpler way. (wikipedia.org)

###### refer

- In order to distinguish number sense in animals from the symbolic and verbal number system in humans researchers use the term numerosity, rather than number, to refer to the concept that supports approximate estimation but does not support an exact representation of number quality. (wikipedia.org)

###### different

- If pure concepts of the understanding (categories) and sensations are radically different, what common quality allows them to relate? (wikipedia.org)

###### sometimes

- In order to test whether a concept is sensible, we sometimes " … go back to perception only tentatively and for the moment, by calling up in imagination a perception corresponding to the concept that occupies us at the moment, a perception that can never be quite adequate to the (general) concept, but is a mere representative of it for the time being. (wikipedia.org)

###### Categories

- Categories represent abstractions of other mathematical concepts. (wikipedia.org)
- However, they must be connected in some way with sensed experience because "… an a priori concept which cannot, as it were, establish any empirical connections is a fraud … the purpose of the Schematism chapter was to show that the categories at least do have satisfactory empirical connections. (wikipedia.org)

###### visual

- This was for example the case in the experiment of Church and Meck, in which rats learned to "add" the number of light flashes to the number of tones to find out the number of expected lever presses, showing a concept of numerosity independent of visual and auditory modalities. (wikipedia.org)
- Artbot - Adult artists explain visual art concepts such as line, color, and composition. (wikipedia.org)

###### general

- For example, "The concept of a dog signifies a rule according to which my imagination can trace, delineate, or draw a general outline, figure, or shape of a four-footed animal without being restricted to any single and particular shape supplied by experience. (wikipedia.org)

###### base

- In her paper for The International Mathematical Journal , Professor Imnotthatold notes that, '…when revealing one's age in normal conversation, it should be possible to stress the desired number while inaudibly mumbling details of the base. (glossynews.com)

###### common

- Examples of intuitive perceptions that are the content of empirical concepts are vague images that are imagined in order to connect a concept with the perceptions from which it was derived as their common feature. (wikipedia.org)

###### thought

- One of the ways that numerical ability is thought to be demonstrated is the transfer of the concept of numerosity across modalities. (wikipedia.org)
- Kant was preoccupied "with bridging the otherwise heterogeneous poles of 'thought' and 'sensation' in the Schematism of the Pure Concepts of the Understanding (A 138/B 177). (wikipedia.org)
- When an empirical concept is said to contain an object, whatever is thought in the concept must be intuited in the mental representation of the object. (wikipedia.org)

###### elements

- This is because "concepts are quite impossible, and are utterly without meaning or signification, unless an object is given for the concepts themselves, or at least for the elements of which they consist. (wikipedia.org)