Correction of Manifolds 1.5 : Manifolds with Boundary Fematika 2026-09-18 | Correction of Manifolds 1.5 : Manifolds with Boundary
Solving a Combinatorics Problem with Group and Number Theory Fematika 2021-07-07 | In this video, I use a group action, Burnside's lemma, Stirling numbers of the first kind, and the rising factorial to prove the number of ways to create an unordered string drawing from an alphabet with replacement.00:00 Intro00:35 Explaining the problem02:44 Introducing permutations04:40 Cycle notation06:40 Group action08:12 Orbits09:30 Fixed points10:20 Burnside's Lemma11:37 Number of fixed points for a permutation15:12 Stirling Numbers of the first kind16:32 Stirling number identity20:28 Examples of Stirling polynomials23:50 Rising factorial identity proof28:14 Final answerTranslate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Manifold 4.2 : Differentials of Smooth Maps and Dimension of the Tangent Space Fematika 2020-04-25 | In this video, I introduce the differentials of a smooth map, prove standard properties of it, and use extensions of smooth maps to prove the dimension of a manifold.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Manifolds 4.1 : Introduction to the Tangent Space Fematika 2020-04-23 | In this video, I introduce the tangent space, and prove that the tangent space of arbitrary euclidean space is the same dimensional (real) vector space.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Algebraic Topology 1.6 : Applications of the Fundamental Group of the Circle Fematika 2020-03-27 | In this video, I introduce some applications of the Fundamental Group of the Circle, which includes the Fundamental Theorem of Algebra, Brouwer's Fixed Point Theorem, and the Borsuk-Ulam Theorem.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Algebraic Topology 1.5 : Covering Maps and the Fundamental Group of the Circle Fematika 2020-03-21 | In this video, I introduce what covering maps are, their property of lifting maps, the construction of unique lifts of paths, and then prove that the fundamental group of the circle is isomorphic to the integers using those lifts.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Algebraic Topology 1.4 : Fundamental Group Fematika 2020-03-17 | In this video, I introduce the fundamental group, and explain the induced isomorphism resulting from a path and the induced homomorphism resulting from a continuous map, proving functorality. I also briefly cover retractions and how their induced homomorphism is surjective.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Algebraic Topology 1.3 : Path Homotopy and Product (Animation Included) Fematika 2019-10-20 | In this video, I introduce the concept of path homotopy, as well as the product of paths. This is in build-up to the fundamental group. I talk about the line homotopy, convex sets, and general theorems regarding products of paths and homotopy.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Category Theory 2.1.1 : Universality of the Comma Category Fematika 2019-09-11 | In this video, I prove a universal property relating to the comma category between two functors. This was filmed a while ago.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
My Interview with BlackPenRedPen : An Afternoon with Fematika Fematika 2019-08-18 | Thanks blackpenredpen! Really appreciate the interview, and for you editing this video.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
An ABSOLUTELY ASTONISHING Infinite Summation | Video for the Younglings Fematika 2019-08-02 | Check out Mu Prime's video as well!: youtube.com/watch?v=b9-377emPKcIn this video, I will be doing the sum of 17/(75*76) + 17*18/(75*76*77) + 17*18*19/(75*76*77*78), question nineteen from a mathematics competition from Hong Kong.6:09 - The actual formula for the sum in general12:34 - The general theorem I will prove (partial sum formula)23:36 - The infinite sum formula25:05 - The solutionTranslate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Category Theory 2.1 : Comma and Slice Categories Fematika 2019-07-25 | In this video, I will introduce the comma category created by two functors, and also the slice and co-slice categories C/a and a/C.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Proof of the Mayer Vietoris Sequence Fematika 2019-07-20 | In this video, I will prove the Mayer-Vietoris sequence and it's more general form. This will assume knowledge of homology, algebraic topology, and chain complexes.Translate This Video :Notes : http://www.math.cmu.edu/~cnewstea/notes/algtop-mayervietoris.pdfPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Category Theory and Competition Projective Geometry | Cross Teaching Fematika 2019-06-15 | Patreon : patreon.com/user/Fematika
Category Theory and Competition Projective Geometry with Essentials of Math | Cross Teaching Fematika 2019-06-14 | In this video, Essentials of Math will be introducing Projective Geometry as it relates to competition math, and I will introduce the basics of Category Theory. Note that the quality of the video is poor up until around 59:00. This is also unedited, I recommend watching my actual series on Category Theory.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Category Theory 1.7: Horizontal Composition and 2-Categories Fematika 2019-04-29 | In this video, I introduce the horizontal composition of natural transformations, the interchange rule, and the basics of 2-Categories/Bicategories.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Limits of Functors | ASMathR Fematika 2019-04-02 | In this video, I introduce limits of functors using ASMR.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Algebraic Topology 1.2 : Homotopy Classes and Properties Fematika 2019-02-26 | In this video, I prove homotopy is an equivalence relation, introduce the homotopy classes of different topological spaces.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Category Theory 1.5 : Properties of Functors, Contravariant Functors, and Subcategories Fematika 2019-02-11 | In this video, I introduce the components of a functor and the hom-set functor on locally-small categories. I then prove that isomorphisms preserve monics, epics, initial objects, and terminal objects. I then introduce contravariant functors, and prove that they reverse the aforementioned properties. I then introduce subcategories, the inclusion functor, and how that defines full subcategories.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Category Theory 1.3 : Properties and Types of Arrows Fematika 2019-02-05 | In this video, I introduce the opposite category, monics, epics, initial object, terminal objects, inverses, idempotent arrows, and more!Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Algebraic Topology 1.1 : Homotopy (Animation Included) Fematika 2019-01-26 | In this video, I will introduce homotopy equivalence, some basic examples of homotopy, and the transitivity of homotopy. I use an animation to intuitively explain these concepts.Translate This Video :Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Complex Magnitude, Argument, and Loci Fematika 2019-01-21 | In this video, I introduce the complex magnitude, and loci. This was a request from BlackPenRedPen.Edited by Sedanimugamez: youtube.com/channel/UClenF9iK45e3oEvmjR2OpZwTranslate This Video : http://www.youtube.com/timedtext_video?v=a_KYJx_nVZ0&ref=shareEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : None yet
Category Theory 1.6 : Natural Transformations Fematika 2019-01-19 | In this video, I will introduce natural transformations between (covariant) functors, and the category of functors.Translate This Video : http://www.youtube.com/timedtext_video?v=YIAaZxGOyl0&ref=shareNotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
General Vector Spaces and Tensors | Wrap it Up! Fematika 2019-01-17 | In this video, I will introduce general vectorspaces over fields, the dual vectorspace, the cobasis, and general tensors.Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=1ReUzrT8n_QNotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Category Theory 1.4 : Functors Definition and Examples Fematika 2019-01-12 | In this video, I introduce functors and types of functors. I also introduce the category of categories. I introduce the power set functor, homology functor, and isomorphic functors.Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=xPd6IxLnsxkNotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Category Theory 1.2 : Examples of Categories and Clarification Fematika 2019-01-08 | In this video, I clarify some terminology, and show some very important examples of categories. This includes the category of groups, sets, topologic spaces, monoids, modules, and rings. I also discuss the relation between categories and individual groups, preorders, matrices, and ordinals.Translate This Video : http://www.youtube.com/timedtext_video?v=pPsWGudxKuQ&ref=shareNotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Presheaves and Sheaves in Category Theory | Wrap it Up! Fematika 2018-12-04 | In this video, I will discuss presheaves and sheaves in the realm of category theory. This also discusses sites, covering families, and matching families.Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=ydS86qPbyJINotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Number Theory 3.2 : Analytic Continuation and Functional Equation for Zeta (ACZ 2/2) Fematika 2018-11-30 | In this video, I prove the analytic continuation of the Riemann Zeta function, as well as its functional equation. I also discuss how to prove that the integral from last time is in fact analytic.Translate This Video : http://www.youtube.com/timedtext_video?v=1ql9hetbuu8&ref=shareNotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Category Theory 1.1 : Introduction to Categories/Metacategories Fematika 2018-11-26 | In this video, I introduce the ideas behind categories and metacategories; specifically their axioms and how they relate to the many structures we've covered before.Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=nMT44uK5ke0Notes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Number Theory 3.1: Analytic Continuation of the Xi/Zeta Function (ACZ 1/2) Fematika 2018-11-24 | In this video, I will prove the analytic continuation of the xi function, which will lead into the continuation of the Riemann Zeta Function.Translate This Video : http://www.youtube.com/timedtext_video?v=epnPu9mx738&ref=shareNotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Abstract Algebra 2.1: Introduction to Rings Fematika 2018-11-20 | In this video, I will introduce rings and basic examples of rings.Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=jesyk7_ti6QNotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
IM BACK Fematika 2018-11-18 | THE LINKS: Translate This Video : http://www.youtube.com/timedtext_video?v=WMgnY41xVa8&ref=shareNotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Manifolds 3.2 : Partitions of Unity on Normal Spaces and Imbeddings Fematika 2018-10-01 | In this video, I introduce general, topological partitions of unity, and how they can be used to imbed compact manifolds into euclidean space.Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=_6etxlOrsusNotes : None yetPatreon : patreon.com/user?u=16481182Teespring : teespring.com/stores/fematikaEmail : fematikaqna@gmail.comDiscord: discord.gg/5z7pgj5Subreddit : reddit.com/r/fematikaCode : github.com/Fematika/Animations
Set Theory 1.4 : Well Orders, Order Isomorphisms, and Ordinals Fematika 2018-09-03 | In this video, I introduce well ordered sets and order isomorphisms, as well as segments. I use these new ideas to prove that all well ordered sets are order isomorphic to some ordinal.Email : fematikaqna@gmail.comDiscord: discord.gg/ePatnjVSubreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : docdro.id/7CsGGpx
Topology 1.7 : More Examples of Topologies Fematika 2018-08-16 | In this video, I introduce important examples of topologies I didn't get the chance to get to. This includes The discrete and trivial topologies, subspace topology, the lower-bound and K topologies on the reals, the dictionary order, and the line with two origins. I also introduce (again) what a Hausdorff topology is.Email : fematikaqna@gmail.comDiscord: discord.gg/ePatnjVSubreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : None yet
Manifolds 3.1 : Partitions of Unity on Smooth Manifolds Fematika 2018-07-20 | In this video, I introduce partitions of unity and smooth bump functions, and prove that every open cover of a smooth manifold has a partition of unity subordinate to it.Email : fematikaqna@gmail.comSubreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : docdro.id/b7tRRCF
Set Theory 1.3 : Ordinals, Supremums, and Minimums (Well Order) Fematika 2018-07-17 | In this video, I prove that a class of ordinals has a minimum and a supremum (as long as it has an upperbound).Email : fematikaqna@gmail.comSubreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : docdro.id/zf39IqL
Measure Theory 3.4: Monotone Convergence Theorem Fematika 2018-07-13 | In this video, I will be proving the Monotone Convergence Theorem for Lebesgue Integrals.Email : fematikaqna@gmail.comSubreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : None yet
The Lambert-W Function and x^y=y^x Fematika 2018-07-03 | In this video, I find the general solution to x^y = y^x and introduce the Lambert-W Function.Email : fematikaqna@gmail.comSubreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : None yet
Abstract Algebra 1.6 : Subgroups, Lagranges Theorem, and the Center Fematika 2018-06-22 | In this video, I introduce Lagranges theorem, using it and other facts to prove many things about groups and their subgroups. I then introduce the center of a group and use it to prove that groups of order prime squared (|G| = p^2) are abelian.Email : fematikaqna@gmail.comSubreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : None yet
Topology 1.6 : Metric Topology Fematika 2018-06-19 | In this video, I introduce the metric topology, and introduce how the topologies it generates align with the standard topologies on Euclidean space.Email : fematikaqna@gmail.comSubreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : None yet
Manifolds 2.3 : Smooth Maps and Diffeomorphisms Fematika 2018-06-14 | In this video, I introduce examples and properties of smooth maps, and show the invariance theorems for diffeomorphisms.Email : fematikaqna@gmail.comCode : github.com/Fematika/AnimationsNotes : None yetPlaylist :
de Rham Cohomology | Wrap It Up! Fematika 2018-06-12 | In this video, I give a summary of what you need to know to understand the de Rham Cohomolgy.Email : fematikaqna@gmail.comCode : github.com/Fematika/AnimationsNotes : None yetPlaylist :
Set Theory 1.2 : Ordinals Fematika 2018-06-08 | In this video, I introduce the Von Neumann construction of the ordinals, including ones that are infinite/transfinite!Email : fematikaqna@gmail.comSubreddit : reddt.com/r/FematikaCode : github.com/Fematika/AnimationsNotes : None yet
Measure Theory 2.4 : Sets of Measure Zero Fematika 2018-05-14 | In this video, I introduce the Cantor Set, and prove that it and countable sets (including the rationals) have measure zero.Email : fematikaqna@gmail.comSubreddit : reddit.com/r/fematikaCode : github.com/Fematika/AnimationsNotes : None yet
Abstract Algebra 1.5 : Examples of Groups Fematika 2018-05-08 | In this video, I introduce many important examples of groups. This includes the group of (rigid) motions, orthogonal group, special orthogonal group, the dihedral groups, and the "finite cyclic group" Z/nZ (or Z_n).Email : fematikaqna@gmail.comCode : github.com/Fematika/AnimationsNotes : None yet
My Notebooks Fematika 2018-05-06 | I go through my notebooks in which I learned math, and discuss some odd stories that went along with them.
Topology 1.5 : Order Topology Fematika 2018-04-29 | In this video, I introduce the order topology and prove that it is Hausdorff.Email : fematikaqna@gmail.comCode : github.com/Fematika/AnimationsNotes : None yet
The Laplacian in Different Coordinates Fematika 2018-04-23 | In this video, I derive the coordinate representation of the laplacian in general coordinate systems.Email : fematikaqna@gmail.comCode : github.com/Fematika/AnimationsNotes : None yet
