Combinatorics | Integer sequences

Spt function

The spt function (smallest parts function) is a function in number theory that counts the sum of the number of smallest parts in each partition of a positive integer. It is related to the partition function. The first few values of spt(n) are: 1, 3, 5, 10, 14, 26, 35, 57, 80, 119, 161, 238, 315, 440, 589 ... (sequence in the OEIS) (Wikipedia).

Video thumbnail

Using the vertical line test to determine if a graph is a function or not

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

Video thumbnail

Definition of a Surjective Function and a Function that is NOT Surjective

We define what it means for a function to be surjective and explain the intuition behind the definition. We then do an example where we show a function is not surjective. Surjective functions are also called onto functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear ht

From playlist Injective, Surjective, and Bijective Functions

Video thumbnail

Injective, Surjective and Bijective Functions (continued)

This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.

From playlist Foundational Math

Video thumbnail

Introduction to Hyperbolic Functions

This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions.

From playlist Using the Properties of Hyperbolic Functions

Video thumbnail

Trigonometry 2 The Trigonometric Functions

Meet the 6 main trigonometric functions of right triangles and some of their identities.

From playlist Trigonometry

Video thumbnail

Adventures in Gapless Topological Phases - Ryan Thorngren

High Energy Theory Seminar Topic: Adventures in Gapless Topological Phases Speaker: Ryan Thorngren Affiliation: Harvard University Date: November 09, 2020 For more video please visit http://video.ias.edu Thorngren-2020-11-09

From playlist IAS High Energy Theory Seminar

Video thumbnail

Lukasz Fidkowski - Symmetry Protected Topological phases, cobordism, and QCA - IPAM at UCLA

Recorded 02 September 2021. Lukasz Fidkowski of the University of Washington presents "Symmetry Protected Topological phases, cobordism, and QCA" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. Abstract: We give an overview of the cobordism classification of

From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter

Video thumbnail

Xie Chen - Symmetry Protected Topological Phases - IPAM at UCLA

Recorded 02 September 2021. Xie Chen of the California Institute of Technology presents "Symmetry Protected Topological Phases" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. Abstract: This talk will give a brief introduction to symmetry protected topologica

From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter

Video thumbnail

The Pi Function - An Overview of Identities

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy All the corresponding Identities used can be f

From playlist Number Theory

Video thumbnail

Sigmoid functions for population growth and A.I.

Some elaborations on sigmoid functions. https://en.wikipedia.org/wiki/Sigmoid_function https://www.learnopencv.com/understanding-activation-functions-in-deep-learning/ If you have any questions of want to contribute to code or videos, feel free to write me a message on youtube or get my co

From playlist Analysis

Video thumbnail

Simple models of Symmetry Protected Topological phases

Simple models of Symmetry Protected Topological phases and Symmetry Enriched Topological phases of bosons in two and three dimensions Discussion Meeting: Quantum entanglement in macroscopic matter URL: http://www.icts.res.in/discussion_meeting/QEM2015/ Dates: Monday 12 Jan, 2015 - Friday

From playlist Discussion Meeting: Quantum entanglement in macroscopic matter

Video thumbnail

Non-Invertible Symmetries and their Representations

IAS High Energy Theory Seminar Topic: Non-Invertible Symmetries and their Representations Speaker: Sahand Seifnashri Affiliation: Member, School of Natural Sciences, IAS Date: September 16, 2022 In the first half of the talk, I will review the notion of non-invertible symmetries and how

From playlist IAS High Energy Theory Seminar

Video thumbnail

New Galaxy Cluster Samples with DES, RASS and SPT: a prelude to eROSITA by Joseph J. Mohr

Program Cosmology - The Next Decade ORGANIZERS : Rishi Khatri, Subha Majumdar and Aseem Paranjape DATE : 03 January 2019 to 25 January 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The great observational progress in cosmology has revealed some very intriguing puzzles, the most i

From playlist Cosmology - The Next Decade

Video thumbnail

Trigonometry - Vocabulary of trigonometric functions

In this video will cover some of the basic vocabulary that you'll hear when working with trigonometric functions. Specifically we'll cover what is trigonometry, angles, and defining the trigonometric functions as ratios of sides. You'll hear these terms again as we dig deeper into the st

From playlist Trigonometry

Video thumbnail

Scott Ahlgren: Algebraic and transcendental formulas for the smallest parts function

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Number Theory

Video thumbnail

Galaxy Cluster Cosmology with the South Pole Telescope by Sebastian Bocquet

Program Cosmology - The Next Decade ORGANIZERS : Rishi Khatri, Subha Majumdar and Aseem Paranjape DATE : 03 January 2019 to 25 January 2019 VENUE : Ramanujan Lecture Hall, ICTS Bangalore The great observational progress in cosmology has revealed some very intriguing puzzles, the most i

From playlist Cosmology - The Next Decade

Video thumbnail

MagLab Theory Winter School 2018: Ryu Shinsei: Quantum Entangle in Conformal & Topological 2

The National MagLab held it's sixth Theory Winter School in Tallahassee, FL from January 8th - 13th, 2018.

From playlist 2018 Theory Winter School

Video thumbnail

Functions of equations - IS IT A FUNCTION

👉 Learn how to determine whether relations such as equations, graphs, ordered pairs, mapping and tables represent a function. A function is defined as a rule which assigns an input to a unique output. Hence, one major requirement of a function is that the function yields one and only one r

From playlist What is the Domain and Range of the Function

Related pages

Modular group | Ramanujan's congruences | Partition (number theory) | Partition function (number theory) | Generating function | Eisenstein series | Number theory | Mock modular form | Dedekind eta function