2:40 - Yeah bro, there is totally not enough content in math. There is only: Proofwriting Discrete mathematics Linear algebra Group theory Ring theory Complex analysis I Topology Field theory Galois theory Euclidean, projective and hyperbolic geometry Algebraic geometry I - varieties Set theory Combinatorial and analytic game theory Representation theory Number theory Module theory Differential topology Differential geometry Category theory I Elliptic curves Algebraic number theory Analytic number theory Commutative algebra Algebraic topology I - homotopy theory Algebraic geometry II - sheaves and schemes Algebraic number theory for cryptography Algebraic topology II - homology and cohomology Algebraic geometry III - coherence Lie groups Riemann surfaces Algebraic topology III - cohomology rings About a trillion different homology and cohomology theories Complex and almost-complex manifolds Modular forms Lie algebras Algebraic topology IV - homotopy type theory Topos theory Lambda calculus nonstandard algebras Algebraic topology V - spectral theory Model theory Algebraic topology VI - homotopical and homological algebra Category theory II - infinity categories Algebraic K theory Vertex operator algebras Mathematical modelling and ODEs Real analysis Dynamical systems Numerical methods Mathematical modelling for neuroscience Space-filling curves PDEs I Functional analysis C*-algebras Nonlinear dynamical systems Calculus of variations Harmonic analysis Morse theory Chaotic dynamical systems Discrete dynamical systems Dispersive PDEs nonlinear Schrodinger equations Riemannian manifolds Optimal transport Ergodic theory Elliptic PDEs Analytic geomtry differential forms Fluid mechanics Symplectic geometry Parabolic PDEs arithmetic geometry Multivariable complex analysis Brownian motion and random walks Numerical methods for time-dependent PDEs symbolic dynamics Conley index theory Tropical geometry Geometric algebra Spacetime algebra Order theory Proof theory Computability theory Complexity theory Automata Code optimization Hyperbolic PDEs Protein folding Topological data analysis Probability theory Mathematical statistics Mathematical modelling of stochastic systems Statistical data analysis Probabilistic forecasting Bayesian statistics Markov chains Measure theory biostatistics Asymptotic statistics Monte Carlo method for approximations and data sampling Databases Measure theoretic probability Stochastic processes Martingales Applied biostatistics Stochastic processes for finance Stochastic analysis Stochastic calculus Multivariate statistics Stochastic PDEs and ODEs Regression methods Statistical genetics statistical machine learning Forensic probability and statistics Causality Statistics for high-dimensional data numerical methods for statistics Removal of random noise Integration on manifolds Quantum computing Random matrix theory Mathematics for thermal engineering Mathematics for electrical engineering Ordinal analysis Nonstandard analysis Algebra for particle physics Control theory Gauge theory Topological K-theory Differential algebra Biomedical mathematics Mathematics for material science Tensor algebra and tensor analysis on manifolds Representations of quivers Hypergraphs and infinite trees Oracle programming Discrete differential geometry Motives Umbral caluclus Adelic groups Meyer-Vietoris theory Hodge theory Representation theory for simple and semisimple Lie algebras Triangulation and tesselation Transcendental number theory Algebraic groups Calabi Yau, cannonically polarized, smooth, complex, projective & toric varieties Stacks in algebraic geometry and topos theory Classification of groups Classification of manifolds Von Neumann algebras Groupoids/magmas, monoids, loops quasigroups, semigroups and other generalizations of groups Langlands program Mathematics for computer graphics
After lvl 25 ypu get to senior teritory where you prove 3 thins: 1) Everything that behaves like an apple can in fact do the basic thins that apples can (Group theory) 2) Somethings behave like an apple even though they are chairs and some things don't even though they are (Topology) 3) How the table should look like to find the apple thay you put there yourself 30' ago (Differential equations) Then you get to Master's teritory, and I can't speak for everyone but I had one in category theory and algebraic topology, which is basically as follows: "I want to know what other things that have nothing to do with the apple can be used to represent the apple and what does this tells us for the apple in comparison to a tractor". I hope I was helpful, now you know the next levels to come.
I beat the Hartshorne Algebraic Geometry Chapter 1 superboss, but the following chapters are still way too overpowered. Level 38 now and I can't remember starting university anymore it was too many theorems ago (the only unit of time which matters at this point, assignment due dates become obsolete past level 35)
The first question of the video “What is a definition for “happy”?”. I disagree with your opinion “they are all right”. I’d argue all options are wrong, each to a greater or lesser extent. a) One can experience joy without happiness. b) Or be happy and content without being cheerful. c) As such, the definition of happy is broader than euphoria. d) And many people feel lonely after winning the lottery.
I’d consider geometric algebra a logical continuation of your previous quests, although you might find it a bit tricky to avoid physics from creeping back into the gameplay
Union of small changes is a big change, that's the fundamental theorem of calculus for all of ya. Derivative is a way of describing change, integral is a way of describing union, it's basically a sum of infinitesimals, when derivative is difference of two infinitely close numbers, divided by infinitesimal f(x + dx) - f(x) ÷ dx f'(x) dx = df = f(x + dx) - f(x) - that's infinitely small change for ya. Sum up full infinity of the changes like that on a segment from a to b, and you'll have f(b) - f(a) change from a to b. Union of small changes is a big change. Always remember that.
Is that… is that a fucking aqworlds reference in my math video? (The probabilities behind the Oracle class was a gateway drug to optimization, actuarial science, and mathematical modeling) Also don’t forget about the homebrew/mods for the game! (math research) Also I’m curious- what math specialization are you in or thinking of doing?
Also linguistic of anagrams :) eleven plus two = twelve plus one :) Of course this course of math will lead you straight to numerology which is forbidding subject of math.
im surprised you're a math major discrediting higher-level mathematics like this. there's so much cool stuff in proof based math and you point to a random combinatorics theorem to show math gets less satisfying
@@pra. Not really discrediting. Currently an upcoming freshman so I’ve dealt with only a bit of proofs as I’ve grown up as an Asian doing a lot of competitive math like AIME / USAMO and stuff. I see your point where I “shame” on it, but that wasn’t really my intention.
I am pretty sure that is Number Theory and not combi. It’s an elementary theorem on quadratic reciprocity, what it’s saying is not exactly higher math like Diophantine Analysis or some shit, a dedicated high school such as myself will not fine it to hard to grasp. But again NT and combi are closely linked so I don’t know if you are wrong but I know I am right. Math is objective but Math is not constant the definitions change.
The really cool thing about Math is that after completing the main story line it turns into an interactive quest where the community can add new content to the game! Plus, there are tons of DLCs that branch of off basically every step of the game progression, in case you want to mix up the story line a bit!
Hey, you sound like “Casually Explained” I can see you’re inspired by him by your channel’s name. Why not try to differentiate a little and experiment and see what works for you! Awesome video btw!
Im at vector calculus and ODEs. Apparently there's some even more advanced stuff like something called "tensor calculus" and "PDEs". Not sure if im looking forward for that
