Mathematics: The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)Mathematical Concepts: Numeric or quantitative entities, descriptions, properties, relationships, operations, and events.Models, Theoretical: Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.Mathematical Computing: Computer-assisted interpretation and analysis of various mathematical functions related to a particular problem.Achievement: Success in bringing an effort to the desired end; the degree or level of success attained in some specified area (esp. scholastic) or in general.Aptitude: The ability to acquire general or special types of knowledge or skill.Algorithms: A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task.Interdisciplinary Studies: Programs of study which span the traditional boundaries of academic scholarship.Learning Disorders: Conditions characterized by a significant discrepancy between an individual's perceived level of intellect and their ability to acquire new language and other cognitive skills. These disorders may result from organic or psychological conditions. Relatively common subtypes include DYSLEXIA, DYSCALCULIA, and DYSGRAPHIA.Test Taking Skills: Skills and strategies, unrelated to the traits a test is intended to measure, that may increase test takers' scores -- may include the effects of coaching or experience in taking tests. (ERIC Thesaurus)Test Anxiety Scale: A self-reporting test consisting of items concerning fear and worry about taking tests and physiological activity, such as heart rate, sweating, etc., before, during, and after tests.Engineering: The practical application of physical, mechanical, and mathematical principles. (Stedman, 25th ed)Biology: One of the BIOLOGICAL SCIENCE DISCIPLINES concerned with the origin, structure, development, growth, function, genetics, and reproduction of animals, plants, and microorganisms.Dyscalculia: Impaired ability in numerical concepts. These inabilities arise as a result of primary neurological lesion, are syndromic (e.g., GERSTMANN SYNDROME ) or acquired due to brain damage.Underachievement: Performance, usually in school work, poorer than that predicted from aptitude and/or intelligence testing.Problem Solving: A learning situation involving more than one alternative from which a selection is made in order to attain a specific goal.Models, Biological: Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.ReadingComputer Simulation: Computer-based representation of physical systems and phenomena such as chemical processes.Technology: The application of scientific knowledge to practical purposes in any field. It includes methods, techniques, and instrumentation.Software: Sequential operating programs and data which instruct the functioning of a digital computer.Science: The study of natural phenomena by observation, measurement, and experimentation.Physics: The study of those aspects of energy and matter in terms of elementary principles and laws. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed)Educational Measurement: The assessing of academic or educational achievement. It includes all aspects of testing and test construction.Knowledge: The body of truths or facts accumulated in the course of time, the cumulated sum of information, its volume and nature, in any civilization, period, or country.Students: Individuals enrolled in a school or formal educational program.DelawareIntelligence: The ability to learn and to deal with new situations and to deal effectively with tasks involving abstractions.Individuality: Those psychological characteristics which differentiate individuals from one another.Dyslexia: A cognitive disorder characterized by an impaired ability to comprehend written and printed words or phrases despite intact vision. This condition may be developmental or acquired. Developmental dyslexia is marked by reading achievement that falls substantially below that expected given the individual's chronological age, measured intelligence, and age-appropriate education. The disturbance in reading significantly interferes with academic achievement or with activities of daily living that require reading skills. (From DSM-IV)Aptitude Tests: Primarily non-verbal tests designed to predict an individual's future learning ability or performance.Child Psychology: The study of normal and abnormal behavior of children.Education of Hearing Disabled: The teaching or training of those individuals with hearing disability or impairment.Child Development: The continuous sequential physiological and psychological maturing of an individual from birth up to but not including ADOLESCENCE.Natural Science Disciplines: The sciences dealing with processes observable in nature.Concept Formation: A cognitive process involving the formation of ideas generalized from the knowledge of qualities, aspects, and relations of objects.Language Arts: Skills in the use of language which lead to proficiency in written or spoken communication.Logic: The science that investigates the principles governing correct or reliable inference and deals with the canons and criteria of validity in thought and demonstration. This system of reasoning is applicable to any branch of knowledge or study. (Random House Unabridged Dictionary, 2d ed & Sippl, Computer Dictionary, 4th ed)Teaching: The educational process of instructing.Curriculum: A course of study offered by an educational institution.Schools: Educational institutions.Intelligence Tests: Standardized tests that measure the present general ability or aptitude for intellectual performance.Intuition: Knowing or understanding without conscious use of reasoning. (Thesaurus of ERIC Descriptors, 1994)Universities: Educational institutions providing facilities for teaching and research and authorized to grant academic degrees.Comprehension: The act or fact of grasping the meaning, nature, or importance of; understanding. (American Heritage Dictionary, 4th ed) Includes understanding by a patient or research subject of information disclosed orally or in writing.Early Intervention (Education): Procedures and programs that facilitate the development or skill acquisition in infants and young children who have disabilities, who are at risk for developing disabilities, or who are gifted. It includes programs that are designed to prevent handicapping conditions in infants and young children and family-centered programs designed to affect the functioning of infants and children with special needs. (From Journal of Early Intervention, Editorial, 1989, vol. 13, no. 1, p. 3; A Discursive Dictionary of Health Care, prepared for the U.S. House of Representatives Committee on Interstate and Foreign Commerce, 1976)Cognition: Intellectual or mental process whereby an organism obtains knowledge.Educational Status: Educational attainment or level of education of individuals.Learning: Relatively permanent change in behavior that is the result of past experience or practice. The concept includes the acquisition of knowledge.Education, Special: Education of the individual who markedly deviates intellectually, physically, socially, or emotionally from those considered to be normal, thus requiring special instruction.Genetic Pleiotropy: A phenomenon in which multiple and diverse phenotypic outcomes are influenced by a single gene (or single gene product.)Education: Acquisition of knowledge as a result of instruction in a formal course of study.Physiology: The biological science concerned with the life-supporting properties, functions, and processes of living organisms or their parts.Language: A verbal or nonverbal means of communicating ideas or feelings.Deafness: A general term for the complete loss of the ability to hear from both ears.Research: Critical and exhaustive investigation or experimentation, having for its aim the discovery of new facts and their correct interpretation, the revision of accepted conclusions, theories, or laws in the light of newly discovered facts, or the practical application of such new or revised conclusions, theories, or laws. (Webster, 3d ed)Models, Educational: Theoretical models which propose methods of learning or teaching as a basis or adjunct to changes in attitude or behavior. These educational interventions are usually applied in the fields of health and patient education but are not restricted to patient care.Memory, Short-Term: Remembrance of information for a few seconds to hours.Executive Function: A set of cognitive functions that controls complex, goal-directed thought and behavior. Executive function involves multiple domains, such as CONCEPT FORMATION, goal management, cognitive flexibility, INHIBITION control, and WORKING MEMORY. Impaired executive function is seen in a range of disorders, e.g., SCHIZOPHRENIA; and ADHD.Language Development: The gradual expansion in complexity and meaning of symbols and sounds as perceived and interpreted by the individual through a maturational and learning process. Stages in development include babbling, cooing, word imitation with cognition, and use of short sentences.Neuropsychological Tests: Tests designed to assess neurological function associated with certain behaviors. They are used in diagnosing brain dysfunction or damage and central nervous system disorders or injury.Affective Symptoms: Mood or emotional responses dissonant with or inappropriate to the behavior and/or stimulus.Adolescent Psychology: Field of psychology concerned with the normal and abnormal behavior of adolescents. It includes mental processes as well as observable responses.Longitudinal Studies: Studies in which variables relating to an individual or group of individuals are assessed over a period of time.MissouriTask Performance and Analysis: The detailed examination of observable activity or behavior associated with the execution or completion of a required function or unit of work.Cognition Disorders: Disturbances in mental processes related to learning, thinking, reasoning, and judgment.Twins: Two individuals derived from two FETUSES that were fertilized at or about the same time, developed in the UTERUS simultaneously, and born to the same mother. Twins are either monozygotic (TWINS, MONOZYGOTIC) or dizygotic (TWINS, DIZYGOTIC).Computational Biology: A field of biology concerned with the development of techniques for the collection and manipulation of biological data, and the use of such data to make biological discoveries or predictions. This field encompasses all computational methods and theories for solving biological problems including manipulation of models and datasets.Systems Biology: Comprehensive, methodical analysis of complex biological systems by monitoring responses to perturbations of biological processes. Large scale, computerized collection and analysis of the data are used to develop and test models of biological systems.History, 20th Century: Time period from 1901 through 2000 of the common era.Statistics as Topic: The science and art of collecting, summarizing, and analyzing data that are subject to random variation. The term is also applied to the data themselves and to the summarization of the data.Sex Factors: Maleness or femaleness as a constituent element or influence contributing to the production of a result. It may be applicable to the cause or effect of a circumstance. It is used with human or animal concepts but should be differentiated from SEX CHARACTERISTICS, anatomical or physiological manifestations of sex, and from SEX DISTRIBUTION, the number of males and females in given circumstances.Models, Statistical: Statistical formulations or analyses which, when applied to data and found to fit the data, are then used to verify the assumptions and parameters used in the analysis. Examples of statistical models are the linear model, binomial model, polynomial model, two-parameter model, etc.Nonlinear Dynamics: The study of systems which respond disproportionately (nonlinearly) to initial conditions or perturbing stimuli. Nonlinear systems may exhibit "chaos" which is classically characterized as sensitive dependence on initial conditions. Chaotic systems, while distinguished from more ordered periodic systems, are not random. When their behavior over time is appropriately displayed (in "phase space"), constraints are evident which are described by "strange attractors". Phase space representations of chaotic systems, or strange attractors, usually reveal fractal (FRACTALS) self-similarity across time scales. Natural, including biological, systems often display nonlinear dynamics and chaos.Attention Deficit Disorder with Hyperactivity: A behavior disorder originating in childhood in which the essential features are signs of developmentally inappropriate inattention, impulsivity, and hyperactivity. Although most individuals have symptoms of both inattention and hyperactivity-impulsivity, one or the other pattern may be predominant. The disorder is more frequent in males than females. Onset is in childhood. Symptoms often attenuate during late adolescence although a minority experience the full complement of symptoms into mid-adulthood. (From DSM-V)Attention: Focusing on certain aspects of current experience to the exclusion of others. It is the act of heeding or taking notice or concentrating.Models, Genetic: Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.Data Interpretation, Statistical: Application of statistical procedures to analyze specific observed or assumed facts from a particular study.Sex Characteristics: Those characteristics that distinguish one SEX from the other. The primary sex characteristics are the OVARIES and TESTES and their related hormones. Secondary sex characteristics are those which are masculine or feminine but not directly related to reproduction.Anxiety: Feeling or emotion of dread, apprehension, and impending disaster but not disabling as with ANXIETY DISORDERS.Program Evaluation: Studies designed to assess the efficacy of programs. They may include the evaluation of cost-effectiveness, the extent to which objectives are met, or impact.
Grillet, Pierre Antoine (2007). Abstract algebra. Graduate texts in mathematics. 242 (2 ed.). Springer. ISBN 978-0-387-71567-4. ... Lang, Serge (2002). Algebra. Graduate Texts in Mathematics. Springer. ISBN 0-387-95385-X.. ... In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the ... Dummit, David S.; Foote, Richard M. (2004). Abstract Algebra (3rd ed.). John Wiley & Sons. ISBN 0-471-43334-9.. ...
In mathematics, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right ... Graded modules and algebras[edit]. Let M be a graded module over a graded algebra, which is generated over a field by its ... Eisenbud, David (1995), Commutative algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics, 150, Berlin ... Weibel, Charles A. (1994). An introduction to homological algebra. Cambridge Studies in Advanced Mathematics. 38. Cambridge ...
Bourbaki, Nicolas (1998), Elements of Mathematics : Algebra I Chapters 1-3, Berlin, New York: Springer-Verlag, ISBN 978-3-540- ... Algebras over fields[edit]. Main articles: Algebra over a field and Lie algebra ... The tensor algebra T(V) is a formal way of adding products to any vector space V to obtain an algebra.[72] As a vector space, ... Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387- ...
Islamic mathematics covered algebra, geometry and arithmetic. Algebra was mainly used for recreation: it had few practical ... Main article: Mathematics in medieval Islam. Islamic mathematicians gathered, organised and clarified the mathematics they ... Maher, P. (1998). From Al-Jabr to Algebra. Mathematics in School, 27(4), 14-15. ... Hogendijk, Jan P.; Berggren, J. L. (1989). "Episodes in the Mathematics of Medieval Islam by J. Lennart Berggren". Journal of ...
Whitney, H. (1933). "Characteristic Functions and the Algebra of Logic". Annals of Mathematics. 34: 405-414. doi:10.2307/ ... Wallis, John (1685). A treatise of algebra. London: John Playford.. *^ Dedekind, Richard (1888). Was sind und was sollen die ... In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple ... Burgin, Mark (2004). "Unified Foundations of Mathematics". arXiv:math/0403186.. *^ Burgin, Mark (2011). Theory of Named Sets. ...
Graduate Texts in Mathematics. 156. Springer. ISBN 0-387-94374-9. Kuratowski, K. (1966). Topology Vol. I. Academic Press. ISBN ... ISBN 3-7643-2428-7. CS1 maint: Multiple names: authors list (link) Arveson, William (1981). An Invitation to C*-Algebras. ... Graduate Texts in Mathematics. Springer-Verlag. ISBN 978-0-387-98412-4. Retrieved 2008-12-04. Ambrosio, L., Gigli, N. & Savaré ... Graduate Texts in Mathematics. 39. New York: Springer-Verlag. ISBN 0-387-90176-0. Bourbaki, Nicolas (1966). Elements of ...
After some algebra, this becomes M. v. 1. =. 2. λ. 1. u. 1. +. 0. M. T. u. 1. =. 0. +. 2. λ. 2. v. 1. {\displaystyle {\begin{ ... Journal of the Society for Industrial and Applied Mathematics. 6 (1): 51-90. doi:10.1137/0106005. JSTOR 2098862. MR 0092215.. ... In linear algebra, the singular-value decomposition (SVD) is a factorization of a real or complex matrix. It is the ... In numerical linear algebra the singular values can be used to determine the effective rank of a matrix, as rounding error may ...
Nathan, M. J. (2002). Mathematics Learning: Algebra. In James W. Guthrie (Ed.) Encyclopedia of Education, Second Edition (Vol. ... Nathan, M. J., and Koedinger, K. R. (2000). Moving beyond teachers' intuitive beliefs about algebra learning. Mathematics ... Nathan, M. J., Kintsch, W., & Young, E. (1992). A theory of algebra word problem comprehension and its implications for the ... Evidence from an early algebra lesson. In Goldman, R., Pea, R., Barron, B. J., and Derry, S. (Eds.) Video Research in the ...
1130-1180 Mathematics: Al-Samawal. An important member of al-Karaji's school of algebra. Gave this definition of algebra: "[it ... Rashed, R (1994). The development of Arabic mathematics: between arithmetic and algebra. London, England.. ... 1135 Mathematics: Sharaf al-Dīn al-Ṭūsī. Follows al-Khayyam's application of algebra of geometry, rather than follow the ... Mathematics: Ibn al-Banna and al-Qalasadi used symbols for mathematics "and, although we do not know exactly when their use ...
If the underlying term ring is a differential algebra, then the algebra of formal power series is also a differential algebra, ... Wikimedia Commons has media related to Series (mathematics).. *. "Series", Encyclopedia of Mathematics, EMS Press, 2001 [1994] ... In this case the algebra of formal power series is the total algebra of the monoid of natural numbers over the underlying term ... Nicolas Bourbaki (1989), Algebra, Springer. : §III.2.11. *^ O'Connor, J.J. & Robertson, E.F. (February 1996). "A history of ...
"Matrix", Encyclopedia of Mathematics, EMS Press, 2001 [1994]. *. Kaw, Autar K., Introduction to Matrix Algebra, ISBN 978-0-615- ... Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, 211 (Revised third ed.), New York: Springer-Verlag, ISBN 978-0-387- ... Greub, Werner Hildbert (1975), Linear algebra, Graduate Texts in Mathematics, Berlin, DE; New York, NY: Springer-Verlag, ISBN ... Schneider, Hans; Barker, George Phillip (2012), Matrices and Linear Algebra, Dover Books on Mathematics, Courier Dover ...
2012). "S. N. Chernikov and the development of infinite group theory". Algebra and Discrete Mathematics. 13 (2): 169-208. ... In mathematics, in the field of group theory, a locally finite group is a type of group that can be studied in ways analogous ... 256-262 Dixon, Martyn R. (1994), Sylow theory, formations and Fitting classes in locally finite groups, Series in Algebra, 2, ... Curtis, Charles; Reiner, Irving (1962), Representation Theory of Finite Groups and Associated Algebras, John Wiley & Sons, pp. ...
2012). "S. N. Chernikov and the development of infinite group theory". Algebra and Discrete Mathematics. 13 (2): 169-208. ... Palmer (2001). Banach algebras and the general theory of *-algebras. p. 1283. For the term, compare Engel's theorem, also on ... ISBN 0-387-90518-9. Palmer, Theodore W. (1994). Banach algebras and the general theory of *-algebras. Cambridge, UK: Cambridge ... Hungerford (1974). Algebra. p. 100. Zassenhaus (1999). The theory of groups. p. 143. Zassenhaus (1999). Theorem 11. p. 143. ...
Algebra and Discrete Mathematics. 13 (2): 169-208. Plotkin, Boris. "Sergei Nikolaevich Chernikov. Memoirs" (PDF). Algebra and ... Journal Algebra Discrete Math. M. Kurosh A.G., Chernikov S.N. (1947) Soluble and nilpotent groups. Uspekhi Math. Nauk 2, number ... Until November 1931 he taught mathematics in a school for workers. From 1930 he was an external student of the Pedagogic ... University of Saint Andrews School of Mathematics and Statistics. Retrieved 7 July 2016. Ershov, Y.L.; et al. (1988). "Sergei ...
Tian JP (2008). Evolution Algebras and their Applications. Lecture Notes in Mathematics. 1921. Berlin; New York: Springer. doi: ... Interdisciplinary Applied Mathematics. 27 (2nd ed.). New York: Springer-Verlag. ISBN 0-387-20191-2. . LCCN 2003065728. OCLC ... The mathematics of genetic drift depend on the effective population size, but it is not clear how this is related to the actual ... genetic drift has no direction and is guided only by the mathematics of chance.[28] As a result, drift acts upon the genotypic ...
... and their Algebra course was designated one of five exemplary curricula for K-12 mathematics educated by the US Department of ... "Middle School Mathematics intervention report: Cognitive Tutor® Algebra I" (PDF). What Works Clearinghouse. whatworks.ed.gov. ... algebra and geometry". PACT's most successful product was the Cognitive Tutor Algebra course. Originally created in the early ... Further, in 2005, Carnegie Learning released Bridge to Algebra, a product intended for middle schools that was piloted in over ...
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Lang, Serge (2002). Algebra. Graduate Texts in Mathematics. 211. Berlin; New York: Springer-Verlag. doi:10.1007/978-1-4613-0041 ... Faticoni, Theodore G. (2012). The Mathematics of Infinity: A Guide to Great Ideas. Pure and Applied Mathematics: A Wiley Series ... Eisenbud, David (1995). Commutative Algebra. Graduate Texts in Mathematics. 150. Berlin; New York: Springer-Verlag. Section 3.3 ... Stillwell, John (2010). Mathematics and Its History. Undergraduate Texts in Mathematics (3rd ed.). Springer. p. 40. ISBN 978-1- ...
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Fundamental structures of algebra and discrete mathematics. p. 128. Pierre Antoine Grillet (2007). Abstract algebra. p. 124. ... In abstract algebra, the field of fractions of an integral domain is the smallest field in which it can be embedded. The ... Ėrnest Borisovich Vinberg (2003). A course in algebra. p. 131. Stephan Foldes (1994). ... Rings, Modules, and Linear Algebra: Hartley, B & Hawkes, T.O. 1970. ...
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Foldes, Stephan (1994). Fundamental Structures of Algebra and Discrete Mathematics. Hoboken: John Wiley & Sons. ISBN ... In mathematics, a structure on a set is an additional mathematical object that, in some manner, attaches (or relates) to that ... In 1939, the French group with the pseudonym Nicolas Bourbaki saw structures as the root of mathematics. They first mentioned ... ISBN 978-0-619-21558-3. Pudlák, Pavel (2013). "Mathematical structures". Logical foundations of mathematics and computational ...
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  • After giving a brief introduction to vertex operator algebras (VOA), I will discuss known examples and the status of the classification of holomorphic VOAs. (arizona.edu)
  • What is needed next is a corresponding interplay with analysis and functional analysis that would extend also to quantum operator algebras , their representations and symmetries . (planetmath.org)
  • Volume II comprises all subjects customary to a first-year graduate course in algebra, and it revisits many topics from Volume I with greater depth and sophistication. (abebooks.com)
  • You can think of this as a small contribution to a discussion about education of programmers and the role of mathematics and other theoretical subjects in it. (speakerdeck.com)
  • Thedistortion of a subalgebra in an algebra also reflects the degree of complexityof the membership problem for the elements of this algebra in this subalgebra.One of our goals here is to investigate, mostly in the case of associative orLie algebras, if a tame filtration of an algebra can be induced from the degreefiltration of a larger algebra. (duhnnae.com)
  • The purpose of the Algebra Seminar this semester is to present an outline of the theory of complex semi-simple Lie algebras. (wmich.edu)
  • The main goal is to reach the point where a novice can understand some structure theory of classical Lie groups and Lie algebras using Dynkin diagrams. (wmich.edu)
  • In this first talk I will recall the classical Wedderburn theory, the role of idempotents in the group algebra, and introduce p-modular systems. (wmich.edu)
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