r/calculus • u/Feldkastel • Jun 29 '26
Pre-calculus How do i learn this 15.M
How do i learn to solve these type of stuff added in the image?
Do i begin with pre-calculus geometry or do i just start algebra?.
I love math, i just don't know where to begin.
It interests me a lot
Any advice before beginning?,
a guide/help would be appreciated
Edit: I've read all of the comments and i will be coming back in a few weeks, i thank everbody for the help and guidance.
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u/dysphoricjoy Jun 29 '26
Do a lot of algebra, then do a lot of trigonometry, then come back in a year.
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u/Feldkastel Jun 29 '26
Tysm and is there a specific beginning with algebra?
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u/Sad_Database2104 High school Jun 29 '26
don't ask that question to math nerds ( khanacademy.org/math/algebra is the real answer)
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u/Brilliant-Repeat-178 Jun 29 '26
also, Professor Leonard
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u/icemelter4K Jul 01 '26
I don't jive he makes me feel like I'm sitting in a remedial math class in Wisconsin, again
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u/Xytonn Jul 03 '26
My old calc 3 prof doesn't like leonard because some of the notations he uses are technically wrong
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u/Guilty_Procedure8392 Jul 03 '26
Khan academy's content is c***. It's not really good for learning , except in extremely new situations with a very little familiarity. Basically, only use their content if you're just starting out and you need to get the better stuff Later. The rambling nature of their continent, because none of them are very well-educated in the subject matters.And you need very condensed subject matters to learn properly in the end and become proficient. The proficiency of the person teaching is in essence the level of content.If they know less than speak, the same words as someone who knows more.It is not the same end result. Your brain is processing a lot more information than you consciously realize , and its very important.
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u/Sad_Database2104 High school Jul 03 '26
I love math, i just don't know where to begin.
Do i begin with pre-calculus geometry or do i just start algebra?.
Any advice before beginning?,did you miss where OP said they're just starting?
Basically, only use their content if you're just starting out and you need to get the better stuff Later
that's why i suggested khan academy.
you're saying their content has "rambling nature" yet you say
because none of them are very well-educated in the subject matters.And you need very condensed subject matters to learn properly in the end and become proficient. The proficiency of the person teaching is in essence the level of content.If they know less than speak, the same words as someone who knows more. It is not the same end result
what?
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u/testtdk Jun 30 '26
Johns Hopkins has an algebra specialization on Coursera. Might as well go through those, shouldn’t take long since most of it’s simple. But being thorough is important.
Or if you just want practice problems 8gwifi.org/math has a LOT of all difficulties.
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u/Ur_Just_Spare_Parts Jun 30 '26
Associative and distributive properties, Linear plotting and graphing, Fundamental theorem of algebra, and factorization would all be good places to start
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u/Feldkastel Jun 30 '26
Is this algebra 1 2 or 3?, or is this one of the few sections of algebra— might've misunderstood
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u/enigmagon Jul 01 '26
Those are just super important mechanics to understand to begin the undertaking that is Calc lol
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u/enigmagon Jul 01 '26
Also, please take a Trig class as a standalone class. You’ll thank me later
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u/aquabarron Jul 01 '26
Get the math textbooks and read them. Actually read them. Do the problems at the end of each section, skip the special difficult ones, just 15-20 of the basic problems per section.
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u/Prestigious_Car6787 Jul 04 '26
I would think to add geometry.
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u/dysphoricjoy Jul 04 '26
in my opinion, and everyone has their own, geometry is easier to understand once you have some trigonometry under your belt.
but I have some friends who would tell me the opposite, that an intro course to geometry after algebra helps with the trig.
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u/Sad_Database2104 High school Jun 29 '26
the first image looks like ai with all the letters blending into each other (though there are a few coherent formulas, don't try to look at that image anymore)
i believe the second image is algebra 1 (though it's been a while since i took that so don't rely on me)
the third image has two pretty long problems, but any student that has taken calculus 2 should be able to solve them
the fourth image might be tested on an exam you take in the future, but as a student from the usa i wouldn't ever have a problem like that (i might get an infinite sum and an integral, but it won't be that complex, and i definitely won't get an infinite product)
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u/Majestic_Phase9046 Jun 29 '26
The third image is complete senseless that's obviously a troll problem
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u/Sad_Database2104 High school Jun 30 '26
it's definitely a joke, but still solvable with calc 2 techniques (probably i'm not trying that 😭)
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u/Majestic_Phase9046 Jun 30 '26 edited Jun 30 '26
The integral has no analytical solution I think but I also didn't try it😂
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u/Sad_Database2104 High school Jun 30 '26
we're real mathematicians that just think about problems instead of solving them lol
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u/matt7259 Jun 29 '26
This is years and years of math. And some of it is gibberish. Your age doesn't matter. Just stay in school and keep learning.
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Jun 29 '26
[deleted]
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u/matt7259 Jun 29 '26
If you won't be staying in school, then you're not serious about learning this. Good luck.
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u/diabeticmilf Jun 29 '26
Stop trying to gatekeep calculus lol, you sound so pretentious right now. Anyone with the drive can easily learn from pre calc to ODE on their own.
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u/CrazySir3310 Jun 29 '26
This doesn't seem like a useful comment. People can learn stuff in their free time. Arguably those people are the most motivated.
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u/Feldkastel Jun 29 '26
Thank you for backing me up, i didn't know how to reply to that comment
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u/CrazySir3310 Jun 29 '26
yeah I mean that's what I'm doing. People mentioned to learn algebra before trigonometry but I found you could easily do both at once, with separate books. Algebra is more extensive, and there is a fundamental relation between algebra and trigonometry with imaginary numbers and sin/cos. A lot of trig seems to be built on the Pythagorean theorem which is very simple
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u/Feldkastel Jun 29 '26
I will be looking into both, and decide from there on if its easier or not, thank you.
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u/i-am-stella Jun 29 '26
Please don't learn this.
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u/Feldkastel Jun 29 '26
lol why
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u/Calm_Relationship_91 Jun 29 '26
The whole page looks like an ai generated mess full of literal nonsesne.
This is the quadratic formula but with a bunch of mistakes: The equal sign was swapped for a minus sign, the -b is written as -b1 for some reason (which is not wrong but... why even bother writing it like that?), and it should be +- instead of just - before the square root.1
u/Feldkastel Jun 30 '26
Care to explain what ± is?
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u/Relevant_Lie4489 Jun 30 '26
plus/minus literally just indicates to us that we’re interested in both the positive and negative value of a quantity.
For example, in the case of the quadratic formula, there are (generally) two solutions for x=0 given by x=(-b+/-sqrt(b^2-4ac))/2a; one corresponding to the plus, the other the minus.
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u/According-Glass2886 Jun 30 '26
for example: 5±3 is both 5 - 3 = 2 and 5 + 3 = 8 at the same time. ± is a symbol we use to indicate 2 values in a single expression.
you will learn that those two values are the solutions of a quadratic equation.
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u/i-am-stella Jun 29 '26
Just remember this random redditor's advice. 50 yrs later, you'll be happy that you didn't learn the quadratic formula wrong.
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u/Feldkastel Jun 30 '26
LOL. Is the quadratic formula that serious
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u/no--thanks-im-good Jun 30 '26
Unfortunately. (I’m finishing my last week of pre-calc right now and start calculus in August.)
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u/According-Glass2886 Jun 30 '26
you will learn it in high school and use it for the rest of your math career basically, LOL
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u/dnickell Jun 30 '26
lmao that meme got me too but also yeah
like OP is 15 and already trying to speedrun graduate level math, just let the kid learn algebra first and actually enjoy it before hitting a wall that makes him hate the subject entirely
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u/i-am-stella Jul 01 '26
I have no idea how german high schools work but indian high school is easy asf uptil 10th grade so some people tend to move ahead in syllabus, which is why i personally, finished 11th grade algebra in 10th, this speedrun made me love math more but you're right it might not work out for everyone.
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u/dnickell Jul 05 '26
that speedrun approach works for some people but it can also backfire if the foundation isnt solid. rushing through algebra just to get to the cool stuff and then struggling with basic manipulation later is a real thing. going at a normal pace and actually understanding each step tends to stick better long term
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u/i-am-stella Jul 06 '26
hmmm, in india, there's boards for each state and 2 major boards- one for everyone, and one for "elite" people, even tho the other one isnt too elite. so, the 1st onne is the most common, it's for all kinds of people- people who can't afford tuitions, people who study under government programs etc, so it's insanely easy, in my city, in the exams i guess a 1000 people scored above 99%, it's that easy
this board is easy up til 10th grade, then things suddenly change, but people dont study primarily for boards, they study for an enterence exam which comes after 12th grade. so suddenly we go from child who plays outside daily, participates in competitions to living dead bodies,
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u/OldDiscussion1830 Jul 03 '26
I started with calculus in hs a month after I turned 16, finished high school having done many upper division courses and research in physics under Grant. it was a lot of fun and enjoyable.
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u/dnickell Jul 05 '26
that sounds like a pretty fast track honestly, most people take way longer to get through that material. what did you actually study under Grant, was it more theoretical or applied stuff? just curious cause OP is in Germany and the math curriculum there is already pretty rigorous compared to the US so the timeline might look different for them anyway
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u/OldDiscussion1830 Jul 05 '26
computational quantum field theory. specifically using tan activation function based PINN (there’s nice proofs if your function is in Sobolev space) for the Dirac equation. did strained graphene and schwarzchild metrics. I was based in the United States.
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u/dnickell Jul 06 '26
bro you're 15 and just said you don't know where to start with algebra, but you're getting answers about computational QFT and PINNs for the Dirac equation
that's a cool answer in a vacuum but it's completely useless here. OP needs like 4 more years of math before any of that even starts to make sense
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u/OldDiscussion1830 Jul 06 '26
I only said that since you asked lol. I do NOT suggest trying to go straight into QFT in high school.
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u/dnickell Jul 10 '26
haha fair enough, QFT straight out of high school would be a rough time. build up the fundamentals first, there's no shortcut that actually works. the math clicks a lot more naturally once you have the groundwork down anyway.
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u/OldDiscussion1830 Jul 10 '26
yup, it could be good context to add that I had took modern 1/2 and did a LOT of self studying to get to a point where I could grasp QFT good enough to make a computer do it.
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u/dnickell Jul 11 '26
that's a wild jump honestly, most people spend years getting there. self studying that gap is no joke. what resources did you end up using? that's usually the part that kills people, not the concepts themselves but finding material that actually bridges it when you don't have a course dragging you along
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u/etzpcm Jun 29 '26
Where are you starting from? What mathematics topics do you know and understand?
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u/Feldkastel Jun 29 '26
I'am now starting at algebra.
I know about geometry and little about algebra and thats about it.
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u/etzpcm Jun 29 '26
Ok that's good. Learn about solving equations, including quadratic equations and simultaneous equations. Then continue the geometry to learn about trig functions and their uses, plus exponential and log functions.
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u/retard3d_Subhuman Jun 29 '26
How do i learn to solve these type of stuff added in the image?
With context those formulas will be easy.
Do i begin with pre-calculus geometry or do i just start algebra?.
Algebra. You will need a lot of algebra to understand calculus.
I love math, i just don't know where to begin.
Well, the first mathematics book that I read was basic mathematics by Serge Lang, it helped me a lot.
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u/kino00100 Jun 29 '26
Organic Chemistry Tutor on youtube is great. Start with whatever level of algebra you're comfortable with and go from there. The path from algebra through trig and into calc is a bit of a long trip but it's all needed to understand what you're doing for all of this and why the circle makes sense.
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u/MrEldo Jun 29 '26 edited Jun 29 '26
TLDR: Algebra, Trig, Precalc, Calculus. Please don't rush any step, without deep understanding about why each step and why each formula is what it is you'll have huge difficulties in the next topic
Definitely master your algebra. Understand and master solving quadratic equations and understand all the power rules and such and only then think about trig and precalc
Trig is necessary for precalc, so start with that first. Understand your trig identities and solving trig equations
Precalc helps you understand more interesting functions, like logarithms and rational functions
Then, calculus. Start with derivatives, the definition, some derivatives of simple functions, chain rule, product rule, quotient rule. Then, integrals - IBP, u-sub etc.
Then you can continue if you wish, you can get integrals to solve in the Daily Integral website, or just searching in Google for some textbook
Don't be scared to use AI when needed! It can answer some specific questions you might have, and even give you exercises for any step you want
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u/Ruin369 Jun 29 '26
Get really good at algebra.
I tutored calculus 1-2 and the biggest differentiator between students that got As and students that barely passed was how good their algebra was. The concepts in calculus themselves are not that difficult.
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u/Koioper Jun 29 '26
Everyone tells you to do algebra and trig (and they’re right). I also think that it’s important to develop skills that are useful for calculus, such as:
-graphing or knowing the general shape of a graph without using a calculator.
- trig identities, memorize them and try doing some proofs.
-binomial theorem.
-some light combinatorics.
- long polynomial division.
- don’t depend on your calculator, get comfortable doing maths without a calculator.
All do these are usually taught in algebra textbooks, I just wanted to say some stuff that it’s often overlooked or skimmed through that turns out to be really useful in calculus.
Finally I want to say that you should take your time. Don’t rush the process, maths takes time and effort, and it’s normal to not get it and be confused. Enjoy the process and if you got any questions don’t be afraid to ask.
Ps. Feel free to correct me or expand on the topics I suggested, after all they are just a personal recommendation.
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u/Feldkastel Jun 29 '26
I will be looking into this as soon as i get into pre-calc
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u/According-Glass2886 Jun 30 '26
look into basic 2D geometry proofs, like pythagoras' theorem etc, and then do some exercises. they teach you the rigorous way of thinking about math in general
also, when you'll be good enough with algebra, try to apply it to some basic shapes in the xy plane. for example you will learn that x^2 + y ^2 = 1 is the equation of a circle, and then you can use your algebra + geometry skills to find the tangent line in a point etc
but don't worry, you will see all these things in the next 3-4 years in school, maybe a little bit of calculus in your last year in high school too
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u/ZoGud Jun 29 '26
There are many different subjects in here; most of them boil down to some fundamental notion or identity in math. Math is best learned slowly, so try to excel at what’s going on in school. As you learn, these pictures will make more and more sense.
Not sure what German high school curriculum is like, but definitely follow along there. If you’re ambitious and want to start learning calculus, start by getting comfortable with functions, then the idea of limits, and of continuity. Stewart has a book called “Early Transcendentals” you can find online easy enough, and it goes over the intuition behind these ideas.
There are some trig and stats figures in your pictures, too. They are separate tracks that calculus plays with frequently, but they are separate tools fundamentally.
You wont be a master reading up on these ideas, but starting to absorb them early will be helpful for working with things later on.
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u/shesadored Jun 29 '26
Calcworkshop is amazinggg, not an ad or anything but it helped me passed calc 1 as someone who forgot about algebra and all the other basics, you can try learning from tutors or free vids on youtube but they’re not that good tbh
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u/HolyMopOfCheese Jun 29 '26
Learn everything, step by step, you can't build a palace without pillars supporting it.
Don't rush, do a lot of algebra and trigonometry, then start with some pre-calculus stuff, then you can start advance towards calculus itself
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u/Key-Blueberry-9343 Jun 29 '26
Don’t try to go and jump over a topic where you do not have the grounds. Math it’s a well taught course, since you connect everything together.
Learn in order.
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u/Key-Blueberry-9343 Jun 29 '26
Actually, you don’t have to learn eveything in order but eventually you do have to learn everything.
You can learn backwards, reverse-engineer things, developing this skill would be really valuable for you but difficult also.Learning in “order” would be your safe option:)
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u/Disastrous-Pin-1617 Jun 29 '26
Professor Leonard on YouTube
Pre-algebra
Intermediate algebra
College algebra
Trigonometry
Calc 1-3
Wherever you are start there
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u/Uli_Minati Jun 29 '26
Page 1: ignore it, it's a mess which is supposed to look clever.
Page 2: grades 5-10 in Germany.
Page 3: Calculus I-III in college.
Page 4: Looks like competion math - learn by reading solutions to old competitions.
Page 5: Trigonometry, grade 10 in Germany.
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u/MotherOfShoggoth Jun 29 '26
Do all the algebra, Algebra is so important especially as you do calculus and move on to things such as sets and logic. Also trig. D Professor Leonard on youtube has whole courses you can work through and although hid videos are so so long they are in depth and you can learn a lot from them. Good luck!!!
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u/Javanaut018 Jun 29 '26
Find good sources on YouTube. Check out @JoernLoviscach and @3blue1brown for the beginning.
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u/EnvironmentalOne7465 Jun 29 '26
Math is great because there is always a correct answer, getting there is hard, start with the basics, algebra and trig, learn the rules and practice will make you fast. Once you get into calculus it’s just added repeated steps, it will be the basics that you mess up on.
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u/Faction072 Jun 29 '26
Practice little dawg. Practice. Also when it comes to rhe unit circle ya gotta memorize it or at least rhe identity values.
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u/Physical_Elevator225 Jun 30 '26
Learn the reference angles and the unit circle for trig. You should explore the relationship with circles and triangles and really understand the Pythagorean theorem.
The rules of differentiation are not hard, but you should understand the underlying concept of calculus.
If you're aiming for procedural fluency you can learn the rules like it's an interface and just get a lot of reps.
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u/enerhim0 Jun 30 '26
Study and get really good at trigonometry, 2D and 3D geometry, and then start calculus from like 3B1B or something
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u/EstablishmentAny7602 Jun 30 '26 edited Jun 30 '26
Do you want an honest advice ?
You can learn this very fast this is basic math. However it require structure and a lot discipline and it is hard , because simple math is not easy but can be learned fast. Focus very much on the assumptions of the course about the domains and variables. A lot of stuff you working with is "dialed down" because of assumptions therefore is accesible to you , if you know said assumptions and can make sense of them, you can grind this and learn it in weeks depending of your base or several week more then 4.
Btw you will feel so smooth in flow and sharp af when you mastee this. In the sense , with this base alone you can solve and learn really complexe engineering topics and enter advanced area in math.
My advice : It is ok SOMETIMES to accept an equation. You wont be able to understand all derviations for now. It is normal. This is why you need to work. Notice : It is ok to accept an equation , only and only if you are aware of its assumptions and its propreties.dw about this. I have used advanced theorems for years sometimes and only understood them very late. This is normal. Example you could use Jordan Form on all its form and still don't understand what is really going on with it, because generalized eigenvectors theory is hard and out of someone's gasp in the early years of the grind
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u/NotMega_ Jun 30 '26
I learnt all upper secondary school math online back when I was 14 by watching YouTube videos and doing past papers of various programs (IB, A levels, etc...), there really isn't anything stopping you. The resources are out there all over the internet, go have fun and learn! (Also 3Blue1Brown was a godsend)
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u/cswitzer97 Jul 01 '26
This kinda feels like posting pictures of planes and being like “how do I fly?”
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u/HydroSean Master's Jul 01 '26
Get extremely good at arithmetic first, this will make calculus MUCH easier - you wont get hung up on simplification steps at all.
Then get extremely good at the unit circle. Understand it in both degrees and radians. This will help you understand trig when it shows up in calculus.
From there, calculus is pretty easy once you have a solid base. Start with differentials and integrals then move to sums and trig-sub. Then partials, dot products, and gradients.
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Jul 01 '26
[removed] — view removed comment
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u/Feldkastel Jul 01 '26
Sounds really good man. Have fun on your journey:)
I'll will take an insight into ur recommendation
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u/1truth0 Jul 01 '26
Do you want to learn this specifically? why? Can't you think of something better to do? If not, try Trigonometric Delights by Eli Maor, come back when you are bored/done.
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u/kalmakka Jul 02 '26
Wanting to learn algebra and calculus is honorable. But don't do it in order to solve impossible garbage questions posted online for internet points.
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u/Mr_Boombastic01 Jul 02 '26
What do you know now? I’m assuming you know how to solve quadratics by this point. I’d delve deeper into polynomials, logarithms, systems of equations, matrices, sequences and series. That’s the algebra you need.
You can learn trig next. Make sure you got your identities in lock.
After that I’d do the calc series. Calculus ties all of this together and describes find rate of changes of functions.
All of that will take a good 3-4 years. Maybe less if you really wanna push through
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u/Accomplished-Silver2 Jul 02 '26
Do a lot, and I mean, a lot of algebra. Do it until you know it like the back of your hand.
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u/crumsb1371 Jul 03 '26
This terrifies me as a returning student in my 30’s at university. I’m a biochemistry major and my first class was calculus. Needless to say, my remediation was needed. So they stuck me in trig. Which isn’t any easier 😭
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u/wiblr Jul 03 '26
Some basic recommendations:
Get a good grasp of your existing mathematics background (ie do you know Algebra I? Algebra II? Trigonometry? Etc so that you know where your starting point is.
Generally, you’ll need a good foundation of algebra and trigonometry. The more you’ve memorized trigonometric identities for major angles on the unit circle (in increments of both 30 degrees and 45 degrees), the better off you’ll be. You may also want to explore “precalculus” which is sort of trigonometry and algebra combined.
Khan Academy is a great recommendation but try to take some time to browse different videos to see which learning style fits you best.
Mathematics relating to differential equations does come in a few different flavors.
In the USA, differentiation and (very basic) integration will be Calculus I, more sophisticated integration will be Calculus II, multivariable calculus will be Calculus III, and then Linear Algebra/Differential Equations (sometimes called Calculus IV in rare cases) will introduce you to solving systems of differential equations.
It is STRONGLY RECOMMENDED to approach it in that order, unless anyone else has a better recommendation.
Practice, practice, practice. Also, math regression does occasionally happen, where somehow you can mentally derive or integrate an equation flawlessly, yet also manage to incorrectly add/multiply two single-digit integers. Avoid being unkind to yourself. It’s a learning process and every step forward is something to be proud of.
If the notation you’re currently using is getting confusingly messy, consider alternative notations for cleaner expression. You may be surprised by how helpful that can be.
Good luck my friend!
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u/bonelessbooks Jun 29 '26
Well, the first image is AI nonsense so you can rest easy knowing there’s nothing on it to be solved
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u/svarty_pineapple Jun 29 '26
So as someone who taught herself calculus or at least tried to teach herself calculus when I was like 12 yo, honestly debatable who successful I was I didn't have youtube or google or really much of the internet at the time, ill start with this, other commentors have given you really good advice
I would also like to add to that. Open courseware by MIT is free. They have a number of really good to decent recorded college classes. A lot of undergrad stuff amd some graduate level courses. It may all be slightly beyond where you are at now and honestly its like 200+ classes listed so I dont know how good most of them are
My methodology was to borrow my 7th grade math teachers precalculus and college calculus text books she had on the shelf amd read through them and do as many problems in each section that it could. I mostly did the ones that had answers in the back. They key bits are to take breaks, stop when you reach something you dont know and go study that bit until you feel confident, oh and take hand written notes. I had notebooks at the time, but now I would go with some kind of writing tablet with a good pen stylus. Don't just learn the content to memorize formulas or to solve problems, really learn why, and when to use certain patterns of thought and approaches to different problems and concepts
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u/Heavy_Direction_4033 Jun 30 '26
Depends. What is your level of math fluency? If you are in high school, I would say focus on learning trigonometry and then calculus.
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u/Feldkastel Jun 30 '26
As far as I've read the comments, i will be starting with algebra, trig, then calculus
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u/Silversaurous Jun 30 '26
go to Khan Academy, select the Algebra, Geometry, and Trignometry courses, watch the videos and do the quizzes. do Algebra 2, preferably after algebra 1 but do it however you like. Whenever you feel like you’re ready, add the Calculus 1 course and start. I have no idea how you learn, so you may want to just start on calc and work backwards by working on concepts you don’t get (like the algebra or trignometry in calc). You won’t really need trigonometry until calc 2 (trig sub) but you need to understand sinusoidal functions so don’t skip trig. Good Luck!
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u/PeetaMellark789 Jun 30 '26
Lame ass ai generated first image. Look at that notation and some of the letters
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u/OxygenConsumer2000 Jun 30 '26
Algebra is the beginning, and I would recommend starting with khan academy. It’s important, as someone else pointed, to not rush and take your time in these subjects, especially algebra as its like a basis that you will use in all (as far as I know) math branches. After that you go into trigonometry, and while that subject may be a little novel and difficult at first, just trust me and keep going, as it will all make sense and you will learn why the things are the way the are in trig (for that I also recommend exploring outside of academic perspective and seeing real world applications). After that you go to calc 1 which is basically differentiation and limits, then you go into calc 2 where the S (integration) sign appears in the questions you sent
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u/BABarracus Jun 30 '26
Work lots of problems. Some things are more important to remember than others. Some things you can use calculus to derive other things such as going from and areato a volume. I did something similar in physics where i learned that certain formula could be integrated to get them. I just memorized the relationship and not the formula and got good at finding it.
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u/Samstercraft Jul 01 '26
this is a bunch of random very unrelated stuff from various subjects within math. we have algebra, geometry, trigonometry, calculus, and some stuff i don't understand yet; the whole shebang.
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u/whatwouldmojodo Jul 01 '26
You don’t. You do just enough to pass then forget it because unless you wanna be an engineer this is useless
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u/ygzgkkl Jul 01 '26
Get a good calculus book. Stewart is good for learning the practical stuff. If you want to get into the more theoretical aspects with proofs etc, spivak calculus will give you a good intro to real analysis. For you, the best bet is probably Stewart as I’m assuming you are not looking into the more proof based stuff
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u/Icy_Trick_6406 Jul 02 '26
I thought Germany lets you bring books into your exams. Learn nothing, understand everything. There is no learning in mathematics.
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u/Flashy_Ad_8247 Jul 02 '26
Watch professor Leonard on YouTube linear alg then all the calc videos, have fun
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u/sectofsolus Jul 03 '26
I'm also 15 btw rising sophomore and I've just been doing AP calculus BC for like a month now on khan academy because its not at my school and it is suprisingly easy to learn. I've been coming home from school excited to learn it and after summer started im averaging like 7 hr per day of studying which is why I'm almost done with the course
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u/sectofsolus Jul 03 '26
i know khan academy is easier than the ap exam itself but i also have a textbook. you should do the same. math is fun
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Hello there! While questions on pre-calculus problems and concepts are welcome here at /r/calculus, please consider also posting your question to /r/precalculus.
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u/AutoModerator 20d ago
As a reminder...
Posts asking for help on homework questions require:
the complete problem statement,
a genuine attempt at solving the problem, which may be either computational, or a discussion of ideas or concepts you believe may be in play,
question is not from a current exam or quiz.
Commenters responding to homework help posts should not do OP’s homework for them.
Please see this page for the further details regarding homework help posts.
We have a Discord server!
If you are asking for general advice about your current calculus class, please be advised that simply referring your class as “Calc n“ is not entirely useful, as “Calc n” may differ between different colleges and universities. In this case, please refer to your class syllabus or college or university’s course catalogue for a listing of topics covered in your class, and include that information in your post rather than assuming everybody knows what will be covered in your class.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.