(1/2) Hi /sci/, how are you guys? First of all: 1-apologies

>>8625977

(2/2)

In my areas of interest I achieved some success, but I am a complete ignorant when it comes down to mathematics. I read popular science books but I know that they are not going to make that much of a difference. So I decided to actually learn math, slowly, from the very beginning.

I am now familiarizing myself with the first concepts of arithmetic, mostly doing exercises of addition, subtraction, multiplication and division. I would like to know what order of subjects and areas is the best one to follow, and also what are the best books to learn, with the best and clearest explanations and the best exercises for one to solve.

Thank you all very much.

>>8625977

OP here.
I forgot to tell you guys what is my ultimate goal: my dream is being capable, many years from now, to understand the universe of modern physics, to actually understand Einstein’s, Schrödinger’s and Heinsenberg’s achievements.

I don’t know if I am capable of actually getting this far, but this is my dream and I will try my best.

>>8626004
That is a long way to go OP.
First off, you should familiarize yourself with the starting concepts and everything that is covered in HS math.
Then advance into precancerous and then into full calc. Some people have problems with series but you should not focus too much into them unless you are especially interested.
Then get into differential equations and differential geometry.
From here on, you will need to learn how to do and read proofs. Take Real analysis courses.
You can also learn complex analysis. It is not mandatory. However, you will learn very valuable techniques that will help you.
From here on, you just have to learn by yourself.

Books:
>The for Dummies series about math surprised me for how good it is. It is way cheaper than a college textbook and covers pretty much all the material.

File: 51+IsecLtWL.jpg (60KB, 330x500px) Image search: [Google]

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>>8626063

Thank you very much.

I have some books that cover the main school course of mathematics. I am using them now, studding something like 2 hours every day.

Is pathetic to be a 30-year-old man doing small addition and subtraction exercises, but my knowledge is indeed very limited.

I plan to keep going alone for 1 or 2 years, and then maybe taking small courses in areas that I find particularly difficult.

It is quite liberating to don’t feel the pressure of your parents and teachers on your back and actually just study for yourself. I can proceed forward with all the slowness without offending anyone with the snail-mucus of my rhythm.

Pic related is a book I discover that seem to be quite valuable when it comes down to the frightening aspects of facing an activity where you failed miserably for so many years.

>>8626098
Another good book series is the
Dover books on mathematics
They are cheap and fairly useful.
However, they tend to be a bit rigorous so you should only use them as a secondary source or as extra material.

>>8625977
>>8626004

For starters

>Learn Elementary Algebra:
Elements of Algebra by Euler
>Supplement it with:
Functions and Graphs by Gelfand, Glagoleva, and Shnol
The Method of Coordinates by Gelfand, Glagoleva, and Kirillov
Algebra by Gelfand and Shen

>Learn Precalculus:
Precalculus with Unit Circle Trigonometry by Cohen
or
Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by Simmons
or
Basic Mathematics by Lang
>Supplement it with:
Trigonometry by Gelfand and Saul
Complex Numbers from A to...Z by Andreescu and Andrica
Complex Numbers and Geometry by Hahn

>Learn Proofs:
Book of Proof by Hammack
>Supplement it with:
How to Solve It: A New Aspect of Mathematical Method by Polya

Then learn Calculus and start learning physics:
http://4chan-science.wikia.com/wiki/Mathematics
http://4chan-science.wikia.com/wiki/Physics_Textbook_Recommendations

I don't have the order of what to learn at the higher up University level, but here is the list of arithmetic to mid-level Sophomore year University.

>1. Arithmetic
>2. Pre-Algebra
>3. Beginning Algebra
>4. Geometry
>5. Intermediate Algebra
>6. Precalculus
>7. College Algebra
>8. Calculus
>9. Discrete Math
>10. Calculus 2
>11. Calculus 3
>12. Linear Algebra
>13. Differential Equations

After that, the courses start going into different directions and don't have much order. I would Google the courses required at Universities and they should have what math courses are required to take in which semester. That should give a decent understanding of the order you should take them in. Hope that helped! Good luck!

>>8628291
I forgot to add Trigonometry. Learn that before Calculus as the Trigonometric Functions will be vital

>>8628291
Pre-calculus should be switched with college algebra.

Though pre-calc is really just college algebra + trig, so if you add trig you could really bypass it altogether. At my uni, it is designed for students who enrolled in calculus but then got crushed because they really didn't have the fundamentals down. The course even started later than all of the others - I think about 3-4 weeks into the semester.

>>8626294
>>8627821
>>8628291

Thanks for all of that.

The list with the order of areas to learn:

>>8628291

Is especially interesting

>>8628472
True, when I took pre calculus thankfully we covered enough Trig to have no issues in Calculus, and the Algebra we learned was pretty much just more and more functions. OP is in a similar situation as me in wanting to take as many courses as possible to learn as much. College Algebra and Trig should come before PreCalc, and then PreCalc may just be able to top it all off perfectly.

>>8626063
>>8627821
>>8628291


>“The greatest thing by far is to be a master of metaphor; it is the one thing that cannot be learnt from others; and it is also a sign of genius, since a good metaphor implies an intuitive perception of the similarity in the dissimilar.” Aristotle, Poetics.

Do you guys mind telling me, if possible, what were the major changes that happened in your minds and world-view after acquiring all this mathematical knowledge? Since my understanding of math is so poor I wonder how much the world and existence will change - and in what aspects the change will or can occur - after I made several years of slow and laborious progress in the study of mathematics (and, if all went well, physics).

What I can say is that my comprehension of reality was forever altered after several years of reading literature, especially poetry. The major change was not a greater knowledge of souls and minds other than my own; it was not the soul-hydration of a continuous immersion in different or more profound philosophies; it was not a greater sense of empathic thinking toward other beings earned by nesting myself inside the brains and the skin of other humans. All of those things will happen in a certain degree if you are willing to read good-quality literature, but that was not the most extreme change in thinking that I experienced. The real change was the one that slowly erupted due to the constant exposure to this figure of speech and central artifact in human language: the metaphor.

The metaphor was the thing that really transformed me. My most profound transformation was one of language, not of philosophy.

>>8631124

When I started to read poetry and pay attention to the metaphors used on it, when I fell in love with metaphoric-textured-language, I realized that all things in the universe seem to be related, that all material things and all abstract concepts and ideas present in themselves aspects of an infinity of other things. Before this slow advent and gradual realization words to me were like hard-shelled entities, all of them firmly individual and separated, like blocks or bricks, that one could use to build phrases and paragraphs.

After my training words became organic entities with no firm envelopment: now they are like cells whose membranes is always oozing its inside fluids of meaning, while at the same time absorbing the meaning-oils of other words. Words to me are something like the gas-planets, that can be perceived as a whole, a single unity, but that, when one actually tries to penetrate them, are made of mists, of nebulous material, a dense smoke of several different meanings and connections (the precise word that identifies this property is “connotations”).

As a result of this mental change now I tend to see things in my day-to-day world experience and generally think on other things, very distant – or near - things that can be summoned by the great power of metaphorical thought. For example, a few days ago I pictured the stars in the night as clothe-moths of light eating the old blanket of the dark, the black flesh of the abyss. Wondering about mathematics and its formulas I pictured the idea that they are something like a diamond-skeleton, the crystal-bones that sustain the organism of the universe. A few days ago I was near the sea, a cold, brownish, frothy and violent sea, and I imagined it like a great bull, foaming and sweating with anger, the sound of the crashing waves was his mooing (a short way of making this metaphor is just to say that the “waves were mooing”), the sea air his breath.

>>8631130

Picturing the break of day from my window I can say something like this about it:

“When the morning tears up the black flesh of the night, and the heavens bleed rust;
When glacial moths of crystal and moist fireflies of the stars
Flee from the sun, the sun who, growling honey of light, lifts his blonde head and the mane of wheat,
Then the soft kingdom of the blankets and warm nest of the beds is abandoned:
The blear and gummy cobweb of sleep and the yawning veneer of dreaming evaporate.”

A cup of coffee can be seen as the solution that the brain uses too make mouthwash and spit out the lazy and rancid jelly of sleepiness. Or it can be seen as the dark and bitter blood, the true nectar of the active God of Production.

Thinking about torture and its effect on the soul - the crippling and maiming of feelings like tranquility, friendship, affection, will-power, confidence, joy, laughter, trust and creativity that continuous torture can produce - I imagined something like this: torture crushes the clitoris of the soul as if it were a soft and fragile grape. Analyzing the relations of the members of the Congress I could not avoid seeing them as wolves dressed in suits.

This happens all the time with me now, this perception that the walls between words and concepts have melted and that their organs and souls are exposed, free to pollinize and be pollinized by other ideas. This was the major change that years of reading literature have produced in me.

I wonder what math has done to your minds in all those years of study.

>>8625977
Does anyone know of rigorous math books?

>>8631156
For what?