>start to learn math as a hobby
>start with Calc 2
>realize I never properly learned integration
>Go back to Calc 1
>realize I never properly learned highschool algebra or logic
>go back to highschool algebra
>realize I don't actually understand arithmetic and might be functionally innumerate
Whats the best way to learn math right, from the very basics of numeracy?
Try khanacademy.com
High School:
• Euclidean geometry, complex numbers, scalar multiplication, Cauchy-Bunyakovskii inequality. Introduction to quantum mechanics (Kostrikin-Manin). Groups of transformations of a plane and space. Derivation of trigonometric identities. Geometry on the upper half-plane (Lobachevsky). Properties of inversion. The action of fractional-linear transformations.
• Rings, fields. Linear algebra, finite groups, Galois theory. Proof of Abel's theorem. Basis, rank, determinants, classical Lie groups. Dedekind cuts. Construction of real and complex numbers. Definition of the tensor product of vector spaces.
• Set theory. Zorn's lemma. Completely ordered sets. Cauchy-Hamel basis. Cantor-Bernstein theorem.
• Metric spaces. Set-theoretic topology (definition of continuous mappings, compactness, proper mappings). Definition of compactness in terms of convergent sequences for spaces with a countable base. Homotopy, fundamental group, homotopy equivalence.
• p-adic numbers, Ostrovsky's theorem, multiplication and division of p-adic numbers by hand.
• Differentiation, integration, Newton-Leibniz formula. Delta-epsilon formalism.
Freshman:
• Analysis in R^n. Differential of a mapping. Contraction mapping lemma. Implicit function theorem. The Riemann-Lebesgue integral. ("Analysis" by Laurent Schwartz, "Analysis" by Zorich, "Theorems and Problems in Functional Analysis" by Kirillov-Gvishiani)
• Hilbert spaces, Banach spaces (definition). The existence of a basis in a Hilbert space. Continuous and discontinuous linear operators. Continuity criteria. Examples of compact operators. ("Analysis" by Laurent Schwartz, "Analysis" by Zorich, "Theorems and Problems in Functional Analysis" by Kirillov-Gvishiani)
• Smooth manifolds, submersions, immersions, Sard's theorem. The partition of unity. Differential topology (Milnor-Wallace). Transversality. Degree of mapping as a topological invariant.
• Differential forms, the de Rham operator, the Stokes theorem, the Maxwell equation of the electromagnetic field. The Gauss-Ostrogradsky theorem as a particular example.
• Complex analysis of one variable (according to the book of Henri Cartan or the first volume of Shabat). Contour integrals, Cauchy's formula, Riemann's theorem on mappings from any simply-connected subset [math] C [/math] to a circle, the extension theorem, Little Picard Theorem. Multivalued functions (for example, the logarithm).
• The theory of categories, definition, functors, equivalences, adjoint functors (Mac Lane, Categories for the working mathematician, Gelfand-Manin, first chapter).
• Groups and Lie algebras. Lie groups. Lie algebras as their linearizations. Universal enveloping algebra, Poincaré-Birkhoff-Witt theorem. Free Lie algebras. The Campbell-Hausdorff series and the construction of a Lie group by its algebra (yellow Serre, first half).
Sophomore:
• Algebraic topology (Fuchs-Fomenko). Cohomology (simplicial, singular, de Rham), their equivalence, Poincaré duality, homotopy groups. Dimension. Fibrations (in the sense of Serre), spectral sequences (Mishchenko, "Vector bundles ...").
• Computation of the cohomology of classical Lie groups and projective spaces.
• Vector bundles, connectivity, Gauss-Bonnet formula, Euler, Chern, Pontryagin, Stiefel-Whitney classes. Multiplicativity of Chern characteristic. Classifying spaces ("Characteristic Classes", Milnor and Stasheff).
• Differential geometry. The Levi-Civita connection, curvature, algebraic and differential identities of Bianchi. Killing fields. Gaussian curvature of a two-dimensional Riemannian manifold. Cellular decomposition of loop space in terms of geodesics. The Morse theory on loop space (Milnor's Morse Theory and Arthur Besse's Einstein Manifolds). Principal bundles and connections on them.
• Commutative algebra (Atiyah-MacDonald). Noetherian rings, Krull dimension, Nakayama lemma, adic completion, integrally closed, discrete valuation rings. Flat modules, local criterion of flatness.
• The Beginning of Algebraic Geometry. (The first chapter of Hartshorne or Shafarevich or green Mumford). Affine varieties, projective varieties, projective morphisms, the image of a projective variety is projective (via resultants). Sheaves. Zariski topology. Algebraic manifold as a ringed space. Hilbert's Nullstellensatz. Spectrum of a ring.
• Introduction to homological algebra. Ext, Tor groups for modules over a ring, resolvents, projective and injective modules (Atiyah-MacDonald). Construction of injective modules. Grothendieck Duality (from the book Springer Lecture Notes in Math, Grothendieck Duality, numbers 21 and 40).
• Number theory; Local and global fields, discriminant, norm, group of ideal classes (blue book of Cassels and Frohlich).
Sophomore (cont):
• Reductive groups, root systems, representations of semisimple groups, weights, Killing form. Groups generated by reflections, their classification. Cohomology of Lie algebras. Computing cohomology in terms of invariant forms. Singular cohomology of a compact Lie group and the cohomology of its algebra. Invariants of classical Lie groups. (Yellow Serre, the second half, Hermann Weyl, "The Classical Groups: Their Invariants and Representations"). Constructions of special Lie groups. Hopf algebras. Quantum groups (definition).
Junior:
• K-theory as a cohomology functor, Bott periodicity, Clifford algebras. Spinors (Atiyah's book "K-Theory" or AS Mishchenko "Vector bundles and their applications"). Spectra. Eilenberg-MacLane Spaces. Infinite loop spaces (according to the book of Switzer or the yellow book of Adams or Adams "Lectures on generalized cohomology", 1972).
• Differential operators, pseudodifferential operators, symbol, elliptic operators. Properties of the Laplace operator. Self-adjoint operators with discrete spectrum. The Green's operator and applications to the Hodge theory on Riemannian manifolds. Quantum mechanics. (R. Wells's book on analysis or Mishchenko "Vector bundles and their application").
• The index formula (Atiyah-Bott-Patodi, Mishchenko), the Riemann-Roch formula. The zeta function of an operator with a discrete spectrum and its asymptotics.
• Homological algebra (Gel'fand-Manin, all chapters except the last chapter). Cohomology of sheaves, derived categories, triangulated categories, derived functor, spectral sequence of a double complex. The composition of triangulated functors and the corresponding spectral sequence. Verdier's duality. The formalism of the six functors and the perverse sheaves.
>>realize I don't actually understand arithmetic and might be functionally innumerate
Explain further
Fuck off.
Junior (cont):
• Algebraic geometry of schemes, schemes over a ring, projective spectra, derivatives of a function, Serre duality, coherent sheaves, base change. Proper and separable schemes, a valuation criterion for properness and separability (Hartshorne). Functors, representability, moduli spaces. Direct and inverse images of sheaves, higher direct images. With proper mapping, higher direct images are coherent.
• Cohomological methods in algebraic geometry, semicontinuity of cohomology, Zariski's connectedness theorem, Stein factorization.
• Kähler manifolds, Lefschetz's theorem, Hodge theory, Kodaira's relations, properties of the Laplace operator (chapter zero of Griffiths-Harris, is clearly presented in the book by André Weil, "Kähler manifolds"). Hermitian bundles. Line bundles and their curvature. Line bundles with positive curvature. Kodaira-Nakano's theorem on the vanishing of cohomology (Griffiths-Harris).
• Holonomy, the Ambrose-Singer theorem, special holonomies, the classification of holonomies, Calabi-Yau manifolds, Hyperkähler manifolds, the Calabi-Yau theorem.
• Spinors on manifolds, Dirac operator, Ricci curvature, Weizenbeck-Lichnerovich formula, Bochner's theorem. Bogomolov's theorem on the decomposition of manifolds with zero canonical class (Arthur Besse, "Einstein varieties").
• Tate cohomology and class field theory (Cassels-Fröhlich, blue book). Calculation of the quotient group of a Galois group of a number field by the commutator. The Brauer Group and its applications.
• Ergodic theory. Ergodicity of billiards.
• Complex curves, pseudoconformal mappings, Teichmüller spaces, Ahlfors-Bers theory (according to Ahlfors's thin book).
Senior:
• Rational and profinite homotopy type. The nerve of the etale covering of the cellular space is homotopically equivalent to its profinite type. Topological definition of etale cohomology. Action of the Galois group on the profinite homotopy type (Sullivan, "Geometric topology").
• Etale cohomology in algebraic geometry, comparison functor, Henselian rings, geometric points. Base change. Any smooth manifold over a field locally in the etale topology is isomorphic to A^n. The etale fundamental group (Milne, Danilov's review from VINITI and SGA 4 1/2, Deligne's first article).
• Elliptic curves, j-invariant, automorphic forms, Taniyama-Weil conjecture and its applications to number theory (Fermat's theorem).
• Rational homotopies (according to the last chapter of Gel'fand-Manin's book or Griffiths-Morgan-Long-Sullivan's article). Massey operations and rational homotopy type. Vanishing Massey operations on a Kahler manifold.
• Chevalley groups, their generators and relations (according to Steinberg's book). Calculation of the group K_2 from the field (Milnor, Algebraic K-Theory).
• Quillen's algebraic K-theory, BGL^+ and Q-construction (Suslin's review in the 25th volume of VINITI, Quillen's lectures - Lecture Notes in Math. 341).
• Complex analytic manifolds, coherent sheaves, Oka's coherence theorem, Hilbert's nullstellensatz for ideals in a sheaf of holomorphic functions. Noetherian ring of germs of holomorphic functions, Weierstrass's theorem on division, Weierstrass's preparation theorem. The Branched Cover Theorem. The Grauert-Remmert theorem (the image of a compact analytic space under a holomorphic morphism is analytic). Hartogs' theorem on the extension of an analytic function. The multidimensional Cauchy formula and its applications (the uniform limit of holomorphic functions is holomorphic).
Specialist: (Fifth year of College):
• The Kodaira-Spencer theory. Deformations of the manifold and solutions of the Maurer-Cartan equation. Maurer-Cartan solvability and Massey operations on the DG-Lie algebra of the cohomology of vector fields. The moduli spaces and their finite dimensionality (see Kontsevich's lectures, or Kodaira's collected works). Bogomolov-Tian-Todorov theorem on deformations of Calabi-Yau.
• Symplectic reduction. The momentum map. The Kempf-Ness theorem.
• Deformations of coherent sheaves and fiber bundles in algebraic geometry. Geometric theory of invariants. The moduli space of bundles on a curve. Stability. The compactifications of Uhlenbeck, Gieseker and Maruyama. The geometric theory of invariants is symplectic reduction (the third edition of Mumford's Geometric Invariant Theory, applications of Francis Kirwan).
• Instantons in four-dimensional geometry. Donaldson's theory. Donaldson's Invariants. Instantons on Kähler surfaces.
• Geometry of complex surfaces. Classification of Kodaira, Kähler and non-Kähler surfaces, Hilbert scheme of points on a surface. The criterion of Castelnuovo-Enriques, the Riemann-Roch formula, the Bogomolov-Miyaoka-Yau inequality. Relations between the numerical invariants of the surface. Elliptic surfaces, Kummer surface, surfaces of type K3 and Enriques.
• Elements of the Mori program: the Kawamata-Viehweg vanishing theorem, theorems on base point freeness, Mori's Cone Theorem (Clemens-Kollar-Mori, "Higher dimensional complex geometry" plus the not translated Kollar-Mori and Kawamata-Matsuki-Masuda).
• Stable bundles as instantons. Yang-Mills equation on a Kahler manifold. The Donaldson-Uhlenbeck-Yau theorem on Yang-Mills metrics on a stable bundle. Its interpretation in terms of symplectic reduction. Stable bundles and instantons on hyper-Kähler manifolds; An explicit solution of the Maurer-Cartan equation in terms of the Green operator.
Specialist (cont):
• Pseudoholomorphic curves on a symplectic manifold. Gromov-Witten invariants. Quantum cohomology. Mirror hypothesis and its interpretation. The structure of the symplectomorphism group (according to the article of Kontsevich-Manin, Polterovich's book "Symplectic geometry", the green book on pseudoholomorphic curves and lecture notes by McDuff and Salamon)
• Complex spinors, the Seiberg-Witten equation, Seiberg-Witten invariants. Why the Seiberg-Witten invariants are equal to the Gromov-Witten invariants.
• Hyperkähler reduction. Flat bundles and the Yang-Mills equation. Hyperkähler structure on the moduli space of flat bundles (Hitchin-Simpson).
• Mixed Hodge structures. Mixed Hodge structures on the cohomology of an algebraic variety. Mixed Hodge structures on the Maltsev completion of the fundamental group. Variations of mixed Hodge structures. The nilpotent orbit theorem. The SL(2)-orbit theorem. Closed and vanishing cycles. The exact sequence of Clemens-Schmid (Griffiths red book "Transcendental methods in algebraic geometry").
• Non-Abelian Hodge theory. Variations of Hodge structures as fixed points of C^*-actions on the moduli space of Higgs bundles (Simpson's thesis).
• Weil conjectures and their proof. l-adic sheaves, perverse sheaves, Frobenius automorphism, weights, the purity theorem (Beilinson, Bernstein, Deligne, plus Deligne, Weil conjectures II)
• The quantitative algebraic topology of Gromov, (Gromov "Metric structures for Riemannian and non-Riemannian spaces"). Gromov-Hausdorff metric, the precompactness of a set of metric spaces, hyperbolic manifolds and hyperbolic groups, harmonic mappings into hyperbolic spaces, the proof of Mostow's rigidity theorem (two compact Kählerian manifolds covered by the same symmetric space X of negative curvature are isometric if their fundamental groups are isomorphic, and dim X> 1).
• Varieties of general type, Kobayashi and Bergman metrics, analytic rigidity (Siu)
Thank you good sir, you are a wealth of knowledge
>Thank you good sir, you are a wealth of knowledge
I'm not a "sir", but you are welcome.
Yeah, only someone autistic enough to type all that out could also be autistic enough to have gender dysphoria
Speed Mathematics Simplified (Dover Books) by Edward Stoddard
Elements of Algebra by Euler
A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre
it's a pasta newredditfriend :^)
Oh look that faggoty pasta.
What is that pasta supposed to achieve?
Anyways, I think most students (american at lest) will go through exactly what you're talking about in calc II. I did and then I went on to tutor calc II and every single person I helped had the exact same problems.
It's because, in all honesty, math teachers throughout k-12 are generally stupid fucks that don't actually understand mathematics and do a shit sloppy job trying to teach their curriculum. It's a catch 22 because anybody who CAN understand and study mathematics and the more advanced applications isn't going to take one of the worst jobs in america (k-12 teacher).
So you stumble through arithmetic, learn a couple algorithms to solve very specific problems, you'll stumble through geometry, algebra, trig, maybe high school offers some calculus.
But you won't know or understand the purpose of complex numbers, what sin and cos functions are aside from how to solve a triangle or see a little wave form and you'll probably be able to factor or expand terms if you're explicitly told to, you might know some exponential and log properties but again. Nothing other than explicit academic exercises.
Calc I is the highest level of math most non stem fields will require therefore it needs to be easy enough for some liberal arts fag to get a "c".
Calc II Is one of your first real stem courses and will expect you to not only have mastered the previous courses but to have somewhat of an understanding so that you can solve problems with fewer directions. You will then go on to actually learn what you where supposed to learn over the last 12+ years in the course of one semester.
>realize I don't actually understand arithmetic
you don't have to understand it, you just have to be able to do it well enough to learn higher concepts.
then you can go back armed with the skills to actually understand arithmetic.
this is basically the way math is taught; in "passes" where you understand a little bit more each time.
which is the best way for kids because their brains need time to develop abstraction anyways
Posting the meme list
There probably aren't more than a dozen little things you have to know from arithmetic. Some are "understand" things and some are just "that's what the notation means" things. But if you skip learning *any* of them, you're completely fucked, even in algebra 1. None of it is hard. Just learn them and then you'll see why you didn't understand crap, and how simple it really is. And stop glossing over shit. You can learn all of it in like a day of study.
redpill me on Lang
>redpill me on Lang
Lang is a meme.
Get a pre-calc textbook and go through that shit. You're probably not as retarded as you think you are; you just forgot a lot of things that you learned in high school.
Koogorov's elements. 10 years of math summed in couple hundred pages that build supreme intuition and also show how each tool is used in physics.
ur a meme
this sounds exactly like my experience
>Explain further
just that counting and understanding numbers terms of an analogy like the number line was completely foreign to me. If someone asked me why 2 negative numbers multiplied are positive, I wouldn't be able to explain. Thinking about division and multiplication besides the algorithms used to solve them was hard for me. Same with absolute values and intervals.
desu I had an awful math education growing up, but I suspect this isn't just me. Most people I know had this crisis in first or second year of STEM where they realized they really didn't understand anything from highschool or before. Like basic geometry, functions, trig etc.. all had to be relearned
>vomit a bunch of math branches
>"learn these"
I think most people who are well off on math kinda miss the point as to why someone doesn't understand math in the first place.If your well off in math you've probably been thinking in a way most people who struggle in math do not,a way that is unnatural to them.
How/what do you teach that supports thinking in math?
Is there a sequel to this? For post-calculus learning?
I think I remember someone posting something of that sort once.
Unironically philosophical symbolic logic. After learning symbolic logic, especially through predicate and sentential logic, with supplementary discourse on metamathematics, math becomes a lot easier.
It's exactly what said.
My experience with taking a first year "weed out" class, as someone that helped his classmates, was that the way the material was taught really sucked. Since it was a combination weed out and "let's show you a little bit of a lot of things", there was minimal or very terse explanations of concepts that were entirely foreign to people that hadn't been doing it on their own already before coming to this class.
Without a grounded explanation for WHY something is, whatever the topic is (whether it's a pointer in C++, a tense in french, a math concept, etc) it has no context. Without context all you can do is understand how different ways of using it gets you different useful results.
That may be practical, in a limited test taking way, but it isn't real understanding and it's very frustrating to have that gap in understanding but have no way to fill it with the materials being provided to you. When your only understanding is a sort of cause / effect or side-effect based understanding, when you get asked a question that relies on the underlying concept you've got absolutely no shot; at best you rely on yet more memorizing of "how to get the right answer for the test" but that's only going to carry you so far; although according to Erica Goldson it'll take you all the way to valedictorian.
sott.net
>why 2 negative numbers multiplied are positive, I wouldn't be able to explain
This is actually somewhat arbitrary. It's a necessary property of the real number system, and there are many calculations (in physics etc.) where this is convenient, but there's no fundamental reason why you couldn't conventionally use a number system where this wasn't the case.
so what is the best way to learn math? (very basic math)
Can definitely confirm this. All the teachers I've had just seemed so uninterested for both teaching and the math they taught. The ones who weren't were just drown out by the noisy class of 30 males in one room , none of whom had any interest in learning or even paying attention. I'll be honest I was one of them and now I have nothing but problems(not getting into desired uni, not understanding the math parts of other subjects etc.). I can't say I hate math but if you fuck up or fall behind one part, nothing following that will make sense, so naturally I gave up like any other average highschooler. I'm trying to go back to all those parts and properly learn this time, the math makes sense and it seems to be easier to just read the book yourself. At least this time you get to learn some theory, whereas every teacher will just skip that and get to the problems so students can cram them
>saying this without explaining what an axiomatic system is
fuck you dickwad
>cauchy-bunyakovsky
Look at this fucking dork.
It's just Cauchy-Schwartz you mouth-breather. We don't give credit to r*ssians here.
cauchy-schwartz-bunyakovsky
If you're looking to review arithmetic, Serre's A Course In Arithmetic is designed for 4th graders to go from adding, subtracting, and multiplying, and so on. I think you might even know square roots by the end. Great intro book, read the whole thing and did every exercise when I was 7.
The wiles-ribet proof of FLT.
that copypasta is a troll right? no one studies that shit in high school.
>american education
LMAO
Thats the average HS curriculum in europe
im eastern european you idiots, went to a gymnasium (secondary for maths & science), our classes are based on Russian and German curriculum.
Its just a joke user
Exactly the same as OP, had calc 1 test and i spent the whole studying time just reviewing basic shit and i dont feel much ready yet, what do? no memers pls
>The wiles-ribet proof of FLT.
>forgetting Taylor
So what's the non meme way to start from the basics and work my way up to calc?
khanacademy is amazing
>one of the worst jobs in america (k-12 teacher).
literally what? highschool teachers get paid a lot. my pre-calc teacher made like $90k
go to high school
>sites.google.com
>Veeky Forums-science.wikia.com/wiki/Mathematics
>wolframscience.com
In this year I bought a book titled "The History of Mathematics". I learned Mathematics is an age old science which dates back thousands of years to the days of primitive man. It'll take you a decade or two to become a master of symbols and numbers just like it'd take a awhile for you to become fluent in a foreign language. People who were trained in numbers back in antiquity, were trained as such from a child and normally became accountants/businessmen. It's important to take your time and relearn everything as you go further into your journey into Advanced Mathematics. You should study Mathematics for at least 60 hours a week for about 4 years and you'll be well beyond the 10,000 hours of practice mark. I recommend learning computers(which is a sub-category of mathematics) as well because it's the newest form of mathematics/science and will help you visualize data.
>In this year I bought a book titled "The History of Mathematics". I learned Mathematics is an age old science which dates back thousands of years to the days of primitive man.
Why must people lie on the internet?
Watch Khan Academy videos on Early Math, Arithmetic, Pre-Algebra, Basic Geometry, Algebra I, Algebra II, and Trigonometry.
Read a Precalculus textbook and do the exercises.
Read an Intro to Proofs book and do the exercises.
Read a Calculus book and do the exercises.
Stop trying to gainsay faggot. At least read the first chapter of the book title "Primitive Origins"
Here we go, this is the shit that I look for on Veeky Forums
Good books on this?
Your shitty graph shows math going back thousands of years though.
Will you be my math gf?
He's probably a gook or spic don't blame him.
work through texts for your own satisfaction and post on Veeky Forums
If you did high school, this is your guide:
1/2
Start by studying language, comunication. Then, semiotics: symbols, semantics, syntaxis, pragmatics.
At this point your will be familiarized with abstractions and the meaning and purpose of symbol combinations. For this first part just google and make your own notes. So the next stage are the calculi: calculus as the process of apply tranformations to some symbols following certain rules. Just the manipulation of symbols and now with this tool you can approach to the laws of thought: logic. For this second part you will need a good book on logic. Now, when after a lot of logic, the next stage is sets theory. You will need another good book. Also, is good to have many complementary books and web resources. At this point you must be familiarized with simple abstract constructions, the structure of mathematical knowledge (axioms, theorems, conjectures, corollaries) and proofs. Proofs are very important: you will start with proofs in logic and then harder proofs on sets.
The next stage is an introduction to the general method of proof: How To Prove It is enough. But before the how to prove it you need use your high school knowledge of math and practice problem solving, mathematical reasoning. There are good books of problem solving too and you can practice mathematical reasoning from admission tests, IQ test, books and courses on preparation, etc.
You will also need reading comprenhension, so work on it from the start.
Well done. Now you can perfect your arithmetic. Also you can start with arithmetic geometry and basics of number theory, conceps like odds, primes... interesting properties of number.
What is a number? Answer yourself.
Then, basic math, freshman algebra. Basic math by Lang for example. You will also learn analytic geometry and some Euclidian in this stage.
2/2
This is the pre-calculus. You will learn trigonometry also. It is useful to learn the basics of statistics, combinatory and probability. The mathematical modelling learned from algebra, proportionality, percentages, the ability of your algorithms and your funtions and its graphic intuition will be very usefull.
You are ready to learn calculus. Also, you are ready to learn linear algebra. You will need to improve your proofs and start to be more rigorous. Study mathematical applications: physics is the obvius option.
And that all. By knowing all of this, you will know whats next and what to choose to learn. Multiple variables calculus, differential equations, topology, analysis, number theory, etc. The culture is for everybody.
Don't forget to study philosophy, the history of the natural world and the humanity. Learn chem and think about life and its evolution. Read Gilgamesh, Illiad, Odyssey, Plato..., Shakespeare, Cervantes..., Goethe, Dostoyevski..., Camus,... and so on.
Welcome and good luck in your path. May the curiosity be with you. Wish the virtue be on your side.
Per aspera ad astra.
List by psycho Verbitskiy. Do you ever read his blog? Man, Misha is really /pol/ freak.
post tits
Khan academy
Giving someone an overly long laundry list with years worth of material is just useless and more likely to scare them away from the subject for good.
Don't have any recomendations, just look at what is generally tought in schools and figure out where is a good place for you to start and work your way up.
Basic algebra is the most important and working with stuff like fractions, exponents and roots should be like second nature for you before you get into anything more complicated.
My precalc teacher is why I am studying math
I learned about summatations, complex numbers, polar coordinates, derivatives, and conics. It was all very interesting and he did a great job of exploring math. I don't really share this experience. I could have taken two AP calculus courses but wasnt sure at the time
Learn logic first, then move onto set theory then do arithmetic, then further abstract it with algebra after you learn that pickup spivak calculus to learn calc then move onto proof based courses/other branches of math.
>If someone asked me why 2 negative numbers multiplied are positive, I wouldn't be able to explain
-a * -b translate to "remove a" time "remove b", it's the same as add "a" times "b" aka => a * b
I think iq89 people get it when you tell them like that.
I think we should not teach substraction as (a - b) but rather as (a + (-b)) just like in my x86 procesor so brainlets can get the simple stuff.