Mathematical modeling | Applied mathematics | Mathematical terminology

Mathematical model

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. (Wikipedia).

Mathematical model
Video thumbnail

(ML 13.6) Graphical model for Bayesian linear regression

As an example, we write down the graphical model for Bayesian linear regression. We introduce the "plate notation", and the convention of shading random variables which are being conditioned on.

From playlist Machine Learning

Video thumbnail

A solar system, a simulation made with Excel

An Excel simulation of the solar system. You can see how things are recursively computed: the mutual gravity force from the locations, the accelerations, the velocities, and finally the updated locations. The solar eclipse is also shown. This is clip is intended to illustrate Chapter 24 Ap

From playlist Physics simulations

Video thumbnail

Natural Models of Type Theory - Steve Awodey

Steve Awodey Carnegie Mellon University; Member, School of Mathematics March 28, 2013 For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

B28 An example problem of a linear model

Here is our first real-world linear problem.

From playlist Differential Equations

Video thumbnail

(ML 13.3) Directed graphical models - formalism (part 1)

Definition of a directed graphical model, or more precisely, what it means for a distribution to respect a directed acyclic graph.

From playlist Machine Learning

Video thumbnail

What is Math Modeling? Video Series Part 5: Getting a Solution

Mathematical modeling uses math to represent, analyze, make predictions, or otherwise provide insight into real world phenomena. This episode, number five in this new seven-part series, guides you through the process of finding a solution to your mathematical model. Here’s where you’ll fi

From playlist M3 Challenge

Video thumbnail

B27 Introduction to linear models

Now that we finally now some techniques to solve simple differential equations, let's apply them to some real-world problems.

From playlist Differential Equations

Video thumbnail

(ML 13.4) Directed graphical models - formalism (part 2)

Definition of a directed graphical model, or more precisely, what it means for a distribution to respect a directed acyclic graph.

From playlist Machine Learning

Video thumbnail

Linear regression

Linear regression is used to compare sets or pairs of numerical data points. We use it to find a correlation between variables.

From playlist Learning medical statistics with python and Jupyter notebooks

Video thumbnail

How can mathematicians contribute to planetary challenges? – ICM2018

IMU Discussion Panels Panel 5 - How can mathematicians contribute to planetary challenges? Moderator: Hans Engler Panelists: Amit Apte, Maria J. Esteban, Pedro Leite da Silva Dias, Edward Lungu, Claudia Sagastizábal © ICM 2018 – International Congress of Mathematicians www.icm2018.or

From playlist IMU Discussion Panels

Video thumbnail

What's the Point of Maths? - with Nira Chamberlain

All around the world children, and even some adults, ask the question: ‘What is the point of mathematics?’. The field of mathematical modelling not only helps answer this question, it can help quench the human thirst for knowledge. Watch the Q&A: https://youtu.be/veMihd8yzwk Subscribe for

From playlist Livestreams

Video thumbnail

Ivan Guo: Financial models of the future

Dr Ivan Guo's research lies predominantly in the areas of stochastic control and financial mathematics. In this interview, he reflects on his SMRI visit and explains the models behind financial mathematics. Find out how transport theory applies to quantitative finance (as well as logisti

From playlist SMRI Interviews

Video thumbnail

Wolfram Physics Project: Working Session Saturday, July 25, 2020 [Metamathematics | Part 2]

This is a Wolfram Physics Project progress update at the Wolfram Summer School. This is a continuation of part two found here: https://youtu.be/x5v3KFFWv2o Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.

From playlist Wolfram Physics Project Livestream Archive

Video thumbnail

Wolfram Physics Project: a Conversation on Current Work (Jan. 26, 2021)

This is a Wolfram Physics Project conversation on our continuing efforts to make progress on the fundamental theory of physics. Begins at 3:00 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Ch

From playlist Wolfram Physics Project Livestream Archive

Video thumbnail

How do mathematicians model infectious disease outbreaks?

Models. They are dictating our Lockdown lives. But what is a mathematical model? We hear about the end result, but how is it put together? What are the assumptions? And how accurate can it be? In our first online only Oxford Mathematics Public Lecture Robin Thompson, Research Fellow in M

From playlist Oxford Mathematics Public Lectures

Video thumbnail

Rinaldo Colombo: "On the Interplay between Mathematical Analysis and Traffic Modeling"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop IV: Social Dynamics beyond Vehicle Autonomy "On the Interplay between Mathematical Analysis and Traffic Modeling" Rinaldo Colombo - Università di Brescia Abstract: Mathematical Analysis offers a variety of to

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

Video thumbnail

What is Math Modeling? Video Series Part 4: Defining Variables

Mathematical modeling uses math to represent, analyze, make predictions, or otherwise provide insight into real world phenomena. After defining the problem statement and making assumptions, defining variables tells modelers exactly the units they are looking for. This creates the basis for

From playlist M3 Challenge

Related pages

Solution concept | Differential equation | Vector space | Deterministic system | Linear equation | Maxwell's equations | Pareto efficiency | Boolean data type | Decision theory | Game theory | All models are wrong | Linear model | Statistical model | Microscale and macroscale models | Mathematical sociology | Regular expression | Real number | Overfitting | Curve fitting | Thermodynamic cycle | Random variable | Constant (mathematics) | Mathematical economics | Deterministic finite automaton | General equilibrium theory | Bayesian statistics | Initial condition | State variable | Occam's razor | Nonparametric statistics | Operations research | Cliodynamics | Sensitivity analysis | Catastrophe theory | Integer | Chaos theory | Extrapolation | Grey box model | Cross-validation (statistics) | Geometry | Speed of light | Loss function | Linear algebra | Neighbour-sensing model | Causality | Linearization | Probability | Particle in a box | Mathematical psychology | Broyden's method | Mathematics | Set (mathematics) | Function (mathematics) | Nonlinear system identification | Artificial neural network | Nash equilibrium | Kleene star | Isaac Newton | Differential operator | Exponential decay | Schrödinger equation | Euclidean geometry | Logistic function | Mathematical optimization | Interpolation | Map projection | Parameter | Language of mathematics | Mathematical diagram | Model theory | Regular language | System identification | Malthusian growth model | Mathematical finance | Agent-based model | Constraint (mathematics) | Newton's method