Mathematical psychology | Applied mathematics
Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task performance). The mathematical approach is used with the goal of deriving hypotheses that are more exact and thus yield stricter empirical validations. There are five major research areas in mathematical psychology: learning and memory, perception and psychophysics, choice and decision-making, language and thinking, and measurement and scaling. Although psychology, as an independent subject of science, is a more recent discipline than physics, the application of mathematics to psychology has been done in the hope of emulating the success of this approach in the physical sciences, which dates back to at least the seventeenth century. Mathematics in psychology is used extensively roughly in two areas: one is the mathematical modeling of psychological theories and experimental phenomena, which leads to mathematical psychology, the other is the statistical approach of quantitative measurement practices in psychology, which leads to psychometrics. As quantification of behavior is fundamental in this endeavor, the theory of measurement is a central topic in mathematical psychology. Mathematical psychology is therefore closely related to psychometrics. However, where psychometrics is concerned with individual differences (or population structure) in mostly static variables, mathematical psychology focuses on process models of perceptual, cognitive and motor processes as inferred from the 'average individual'. Furthermore, where psychometrics investigates the stochastic dependence structure between variables as observed in the population, mathematical psychology almost exclusively focuses on the modeling of data obtained from experimental paradigms and is therefore even more closely related to experimental psychology, cognitive psychology, and psychonomics. Like computational neuroscience and econometrics, mathematical psychology theory often uses statistical optimality as a guiding principle, assuming that the human brain has evolved to solve problems in an optimized way. Central themes from cognitive psychology (e.g., limited vs. unlimited processing capacity, serial vs. parallel processing) and their implications are central in rigorous analysis in mathematical psychology. Mathematical psychologists are active in many fields of psychology, especially in psychophysics, sensation and perception, problem solving, decision-making, learning, memory, language, and the quantitative analysis of behavior, and contribute to the work of other subareas of psychology such as clinical psychology, social psychology, educational psychology, and psychology of music. (Wikipedia).
Logic: The Structure of Reason
As a tool for characterizing rational thought, logic cuts across many philosophical disciplines and lies at the core of mathematics and computer science. Drawing on Aristotle’s Organon, Russell’s Principia Mathematica, and other central works, this program tracks the evolution of logic, be
From playlist Logic & Philosophy of Mathematics
Quantum Mechanics -- a Primer for Mathematicians
Juerg Frohlich ETH Zurich; Member, School of Mathematics, IAS December 3, 2012 A general algebraic formalism for the mathematical modeling of physical systems is sketched. This formalism is sufficiently general to encompass classical and quantum-mechanical models. It is then explained in w
From playlist Mathematics
Formal Definition of a Function using the Cartesian Product
Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid
From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)
Number theory Full Course [A to Z]
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure #mathematics devoted primarily to the study of the integers and integer-valued functions. Number theorists study prime numbers as well as the properties of objects made out of integers (for example, ratio
From playlist Number Theory
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From playlist Science Unplugged: Mathematics
In this talk, we will define elliptic curves and, more importantly, we will try to motivate why they are central to modern number theory. Elliptic curves are ubiquitous not only in number theory, but also in algebraic geometry, complex analysis, cryptography, physics, and beyond. They were
From playlist An Introduction to the Arithmetic of Elliptic Curves
What Are Numbers? Philosophy of Mathematics (Elucidations)
What is mathematics about and how do we acquire mathematical knowledge? Mathematics seems to be about numbers, but what exactly are numbers? Are numbers and other mathematical objects something discovered or invented? Daniel Sutherland discusses some of these issues in the philosophy of ma
From playlist Logic & Philosophy of Mathematics
The problem with `functions' | Arithmetic and Geometry Math Foundations 42a
[First of two parts] Here we address a core logical problem with modern mathematics--the usual definition of a `function' does not contain precise enough bounds on the nature of the rules or procedures (or computer programs) allowed. Here we discuss the difficulty in the context of funct
From playlist Math Foundations
The Scientific Method and the question of "Infinite Sets" | Sociology and Pure Maths| N J Wildberger
Let's get some kind of serious discussion going about the differences in methodology and philosophy between the sciences and mathematics, and how these differences manifest themselves in the attitude towards the logical foundations of mathematics. In particular we look at a bulwark notio
From playlist Sociology and Pure Mathematics
Learnability can be undecidable | AISC
For slides and more information on the paper, visit https://aisc.ai.science/events/2019-06-17/ Discussion lead: Abdulrahman Al-lahham Discussion facilitator: Mehdi Garrousian
From playlist Math and Foundations
Univers Convergents 2016 - séance 1/6 - "A Beautiful Mind"
A Beautiful Mind de Ron Howard (USA - 2001 - 2h15) avec Russell Crowe, Ed Harris, Jennifer Connelly Mardi 26 janvier 2016 - 19h30 John Forbes Nash Jr (1928-2015) est un des plus grands génies mathématiques du XXème siècle. Chercheur surdoué, il est le père d’une « théorie économiq
From playlist Ciné-Club Univers Convergents
What Matters to Me and Why: Elizabeth Loftus
Recorded on October 8, 2014. Distinguished Professor Elizabeth Loftus is renowned for her groundbreaking work on the malleability of human memory. She holds faculty positions in the schools of Social Ecology, Social Sciences and Law. Her 30 years of research have focused on the misinforma
From playlist What Matters to Me and Why
TrevTalks: My University Experience
In this TrevTalks, we talk about my university experience and how its affected my teaching both on YouTube and in real life. It's a little rambly as this is the first episode, but we'll get better! Join this channel to get access to perks: https://www.youtube.com/channel/UCGYSfZbPp3BiAFs5
From playlist TrevTalks
Re-Imagining the Social Sciences in the Age of AI - March 4, 2020
Re-Imagining the Social Sciences in the Age of AI: A Cross-Disciplinary Conversation Wednesday, March 4 5:30 p.m. Wolfensohn Hall Co-organized by the School of Mathematics and the School of Social Sciences, this public event will feature two short talks about the transformational possibi
From playlist Mathematics
John McCarthy (1927-2011): Artificial Intelligence (complete) - Thinking Allowed -Jeffrey Mishlove
Great news!! Now watch every title and guest in the Thinking Allowed Collection, complete and commercial free. More than 350 programs now streaming. Visit http://thinkingallowed.vhx.tv Start today. Cancel any time. Use promo code THINKNOW for a 50% discount for your first month. http://w
From playlist AI talks
Algorithms That Control Our Lives - with David Sumpter
In a world of fake news, Facebook scandals and psychological warfare, mathematician David Sumpter investigates how much influence algorithms truly have over our behaviours. Subscribe for regular science videos: http://bit.ly/RiSubscRibe David's book "Outnumbered: From Facebook and Google
From playlist Mathematics
What's Going on in Behavioral Finance? A Survey of the Latest Ideas - N. Barberis - 1/31/2020
"What's Going on in Behavioral Finance? A Survey of the Latest Ideas" Nicholas C. Barberis, Stephen and Camille Schramm Professor of Finance, Yale School of Management Abstract: The field of behavioral finance tries to make sense of financial data using models that make psychologically ac
From playlist HSS Caltech + Finance 2020
Prejudices Are Harder to Shake Than You Think, with Heidi Grant Halvorson | Big Think
Watch the newest video from Big Think: https://bigth.ink/NewVideo Join Big Think Edge for exclusive videos: https://bigth.ink/Edge ---------------------------------------------------------------------------------- Can stereotypes be useful? Sometimes they can be, even though a lot of the
From playlist Best Videos | Big Think
Frege, Russell, & Modern Logic - A. J. Ayer & Bryan Magee (1987)
In this program, A. J. Ayer discusses the work of Gottlob Frege, Bertrand Russell, and modern logic with Bryan Magee. This is from the 1987 series on great philosophers. #Philosophy #Bryanmagee #BertrandRussell
From playlist Bryan Magee Interviews - The Great Philosophers (1987)
Putting an opinion on YouTube - what could possibly go wrong! This is a bit more bloggy than I usually like to do. I'll be back next time with some proper mathematics. "What is the point of mathematics?"
From playlist My Maths Videos