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File: 1608527960881.pdf ( 1.12 MB , (Undergraduate texts in ma….pdf )

All good communists study math.

What are you studying right now? What is your favorite field of mathematics and why?

Personally, I really like the book "Linear Algebra Done Right" by Sheldon Axler. It is on Libgen if you are interested and I attached a pdf.

95 posts and 19 image replies omitted. Click reply to view.What are you studying right now? What is your favorite field of mathematics and why?

Personally, I really like the book "Linear Algebra Done Right" by Sheldon Axler. It is on Libgen if you are interested and I attached a pdf.

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Do any of you guys have an interest in a thread where we go through sections of a textbook on linear algebra together and return to the thread at least once a week to discuss what we learned. I don't think this would necessary for me to learn the material, and I intend to learn it anyway, but I do think learning would be more fun this way.

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File: 1608528258665.png ( 3.68 KB , 276x64 , bessel.PNG )

this is now an applied math thread.

abstractists gtfo

Post ODEs/PDEs

abstractists gtfo

Post ODEs/PDEs

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File: 1608528258871.png ( 160.57 KB , 1239x131 , Capture.PNG )

>>2922

many many courses on youtube.

if you want something more structured and gamified start with KhanAcademy.org

The calculus playlist is great.

many many courses on youtube.

if you want something more structured and gamified start with KhanAcademy.org

The calculus playlist is great.

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>>359

Do you happen to know any good courses online or whatever on discrete math? I found it pretty interesting but my professor was NOT GOOD at explaining the material and since COVID happened we kind of rushed through the class so I left feeling like I didn't entirely understand all of it

Do you happen to know any good courses online or whatever on discrete math? I found it pretty interesting but my professor was NOT GOOD at explaining the material and since COVID happened we kind of rushed through the class so I left feeling like I didn't entirely understand all of it

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Can any mathsanon explain to me how to actually understand math? Because I just don't seem to master the tasks, that require you to truly understand the Essence of Maths. The only way I solve those Tasks, is when I look at the Solutions and this can't be the Point though, am I right?.

t.Fag who studies Chemical Engineering

t.Fag who studies Chemical Engineering

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>>4741

You do it every day and at some unknown point it just becomes an extension of your mind. The essence can only come from solving problems, usually with other people to get different perspectives, and creating a set of skills which you can call upon to solve problems.

I remember in middle school trying to desperately remember which axis is the x and the y, and how linear equations work. However these attempts are actually counterproductive IMO. At a certain points of maths you let go of trying to 'get' it, and just move on, then after solving future problems it may come to you.

You do it every day and at some unknown point it just becomes an extension of your mind. The essence can only come from solving problems, usually with other people to get different perspectives, and creating a set of skills which you can call upon to solve problems.

I remember in middle school trying to desperately remember which axis is the x and the y, and how linear equations work. However these attempts are actually counterproductive IMO. At a certain points of maths you let go of trying to 'get' it, and just move on, then after solving future problems it may come to you.

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>>4741

You just do it. You want to develop a certain set of skills which are useful in the sense that, when solving problems you always ask yourself

– why am I doing this?

– what happens without this assumption?

– what happens with this assumption?

– why does method work for a finite case but an infinite?

– where have I seen similar structures as this?

and so on. It's a skill really, took me 3 years to get somewhat good at it.

You just do it. You want to develop a certain set of skills which are useful in the sense that, when solving problems you always ask yourself

– why am I doing this?

– what happens without this assumption?

– what happens with this assumption?

– why does method work for a finite case but an infinite?

– where have I seen similar structures as this?

and so on. It's a skill really, took me 3 years to get somewhat good at it.

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File: 1626119874805.jpg ( 122.01 KB , 1280x720 , E3Z_AQtUUAABrAJ.jpg )

What the best way to learn math when you suck at it ?

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>>6408

Mix it with programming IMO. Learn Mathematica or something while learning math. Mathematica actually comes bundled with tutorials that basically teach you a lot of typical math to show how to use the language. But I think it kind of gives you tools to start playing around with math for projects you might have, so the practical applications give you problems to solve that help internalize what you’re learning.

Mix it with programming IMO. Learn Mathematica or something while learning math. Mathematica actually comes bundled with tutorials that basically teach you a lot of typical math to show how to use the language. But I think it kind of gives you tools to start playing around with math for projects you might have, so the practical applications give you problems to solve that help internalize what you’re learning.

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>>6408

If there exist such magical pedagogical solution, you would have heard of it by now. The only way is plowing through. Read and write along the solution manual if you must. You can't learn anything abstract this way but familiarizing differential calculus is just a matter of grit

If there exist such magical pedagogical solution, you would have heard of it by now. The only way is plowing through. Read and write along the solution manual if you must. You can't learn anything abstract this way but familiarizing differential calculus is just a matter of grit

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>>6408

Try Basic Mathematics by Serge Lang

https://4chan-science.fandom.com/wiki/Mathematics#Precalculus

https://betterexplained.com/articles/developing-your-intuition-for-math/

Try Basic Mathematics by Serge Lang

https://4chan-science.fandom.com/wiki/Mathematics#Precalculus

https://betterexplained.com/articles/developing-your-intuition-for-math/

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File: 1627579163473.jpg ( 132.41 KB , 1502x1127 , Godel-Theorem-1.jpg )

What are the material implications of quantum computers on Gödel's Incompleteness theorum?

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File: 1639946499053.png ( 6.05 KB , 740x380 , proof.png )

>>390

pink = all - 4 green = red + blue

>>404

The rocket pigs version: https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/

>>493

>differs from sets to avoid Russel's paradox?

The standard solution is based on von Neumann's work and predates category theory. Cantor's naive sets are renamed to classes. Classes are partitioned into sets and proper classes. Sets are those classes that can be built up using ZFC, which removes unrestricted comprehensions. You can no longer take "all X [with P]", you have to take "all X from S [with P]" where S is already a set. The question becomes whether the class of all sets is a set. The resolution to Russell's paradox is to provide the negative answer by becoming the proof that the class of all sets is a proper class rather than a set.

pink = all - 4 green = red + blue

>>404

The rocket pigs version: https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/

>>493

>differs from sets to avoid Russel's paradox?

The standard solution is based on von Neumann's work and predates category theory. Cantor's naive sets are renamed to classes. Classes are partitioned into sets and proper classes. Sets are those classes that can be built up using ZFC, which removes unrestricted comprehensions. You can no longer take "all X [with P]", you have to take "all X from S [with P]" where S is already a set. The question becomes whether the class of all sets is a set. The resolution to Russell's paradox is to provide the negative answer by becoming the proof that the class of all sets is a proper class rather than a set.

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File: 1641369349530.jpg ( 38.67 KB , 843x698 , bordigamath.jpg )

Just saying, Bordiga was an engineer. Makes sense, he was autistically literal and uncompromising like a STEMy vs the artsy-fartsy Gramsci who spawned generations of culturally obsessed navel-gazing "Marxists" with his post-hoc "theories" justifying his failed politics.

This is why I love Bordiga, he does math so I don't have to.

This is why I love Bordiga, he does math so I don't have to.

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>>341

I think everyone who is interested in math should study linear algebra algebraically so that they can know duality (by studying dual space), Erlangen program and the foundation of non-Euclidean geometry (by studying bilinear forms), Lie groups (by studying classical groups), representation theory (by noting that S_n is isomorphic to the group of permutation matrices so that every finite group is isomorphic to a matrix group.), etc. Of course it could be challenging but it would give them more mathematical maturity than randomly studying tons of other fields.

I think everyone who is interested in math should study linear algebra algebraically so that they can know duality (by studying dual space), Erlangen program and the foundation of non-Euclidean geometry (by studying bilinear forms), Lie groups (by studying classical groups), representation theory (by noting that S_n is isomorphic to the group of permutation matrices so that every finite group is isomorphic to a matrix group.), etc. Of course it could be challenging but it would give them more mathematical maturity than randomly studying tons of other fields.

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>>493

>Is Elements good?

It is really good for your free time. For a degree, it is useless.

Some parts of Elements are really mind blowing. For example, he understands number theory by geometry. For him, the number '1' is the same as a segment of which the length is 1, "a divides b" means one can measure a segment 'b' by a segment 'a' so that the greatest common divisor means the greatest common measure by which one can measure both 'a' and 'b', etc.

>Is Elements good?

It is really good for your free time. For a degree, it is useless.

Some parts of Elements are really mind blowing. For example, he understands number theory by geometry. For him, the number '1' is the same as a segment of which the length is 1, "a divides b" means one can measure a segment 'b' by a segment 'a' so that the greatest common divisor means the greatest common measure by which one can measure both 'a' and 'b', etc.

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>>489

Category theory is a must if you are into some fields like algebraic geometry, number theory, topology, etc. In those fields, people use it more than set theory.

The power of category theory comes from its relativism, generality, intertwining many fields into one. Unlike set theory, you can map topological spaces to groups, their homeomorphisms to homomorphisms in category theory. Of course you can do like that with any other mathematical objects. And you can build a category theory without objects (in fact, the identity morphisms are sufficient to replace all the objects) so you can get all the property of objects not from the objects themselves but only from their relations. Thus you can get result by only drawing some diagrams. This is called "Abstract nonsense" (https://en.wikipedia.org/wiki/Abstract_nonsense).

Category theory is a must if you are into some fields like algebraic geometry, number theory, topology, etc. In those fields, people use it more than set theory.

The power of category theory comes from its relativism, generality, intertwining many fields into one. Unlike set theory, you can map topological spaces to groups, their homeomorphisms to homomorphisms in category theory. Of course you can do like that with any other mathematical objects. And you can build a category theory without objects (in fact, the identity morphisms are sufficient to replace all the objects) so you can get all the property of objects not from the objects themselves but only from their relations. Thus you can get result by only drawing some diagrams. This is called "Abstract nonsense" (https://en.wikipedia.org/wiki/Abstract_nonsense).

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File: 1665011491488.pdf ( 1.23 MB , 197x300 , An Introduction to Formal ….pdf )

I want to learn why, when logical paradoxes exist, we can be certain proven facts are true and not logical paradoxes. I have An Introduction To Formal Logic (attached) and A Modern Formal Logic Primer (https://tellerprimer.ucdavis.edu/); will these help me? If not, what can help me?

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>>7389

No, I want an explanation of why we can use logic to determine what is true and what is not given that paradoxes exist. Logically there shouldn't be paradoxes and everything should either be true, false or meaningless but this isn't the case (Liar's paradox for example, http://tdx37ew3oke5rxn3yi5r5665ka7ozvehnd4xmnjxxdvqorias2nyl4qd.onion/wiki/List_of_paradoxes?lang=en#Logic for more) so how and why can we use logic to prove things when it clearly fails at some points? I also asked if the books I have will help me answer these questions. I asked nothing about*why* paradoxes exist but asked about their implications on the validity of logical deductions and if the books I have will help me answer this question or give me some required knowledge before it can be and if these books do neither then I asked for some books that will.

No, I want an explanation of why we can use logic to determine what is true and what is not given that paradoxes exist. Logically there shouldn't be paradoxes and everything should either be true, false or meaningless but this isn't the case (Liar's paradox for example, http://tdx37ew3oke5rxn3yi5r5665ka7ozvehnd4xmnjxxdvqorias2nyl4qd.onion/wiki/List_of_paradoxes?lang=en#Logic for more) so how and why can we use logic to prove things when it clearly fails at some points? I also asked if the books I have will help me answer these questions. I asked nothing about

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>>7395

>Liar's paradox

<This statement is false

is self referencing, if you feed it into a logic interpreter it will cause an infinite statement expansion, and the interpreter will never actually get to the point where it can perform any logic operations.

If you want to know about this, read about Godel's incompleteness theorem or in computer science the halting problem.

>Liar's paradox

<This statement is false

is self referencing, if you feed it into a logic interpreter it will cause an infinite statement expansion, and the interpreter will never actually get to the point where it can perform any logic operations.

If you want to know about this, read about Godel's incompleteness theorem or in computer science the halting problem.

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>>7395

Because everything we know revolves around a series of assumptions apriori: Things like laws of physics, fields, assumptions about foundational asthmatic. There are things that are true simple because they appear to be the most reasonable explanations for what we observe. Even though our methods do not appear to be perfect they have repeatedly delivered the most reasonable and logical explanations for our observations for centuries and thus demand the benefit of the doubt in the continued use.

The only way this could be challenged is if there was a system of logic superior to the one we currently have today, which, is completely possible, so, if you have a methodology of logic greater than what we currently have, or, a scientific methodology better than the methodology we currently have then explain it….

It's kind of like democracy: It isn't perfect but it's the best we have.

Because everything we know revolves around a series of assumptions apriori: Things like laws of physics, fields, assumptions about foundational asthmatic. There are things that are true simple because they appear to be the most reasonable explanations for what we observe. Even though our methods do not appear to be perfect they have repeatedly delivered the most reasonable and logical explanations for our observations for centuries and thus demand the benefit of the doubt in the continued use.

The only way this could be challenged is if there was a system of logic superior to the one we currently have today, which, is completely possible, so, if you have a methodology of logic greater than what we currently have, or, a scientific methodology better than the methodology we currently have then explain it….

It's kind of like democracy: It isn't perfect but it's the best we have.

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>>7395

>Logically there shouldn't be paradoxes

Formal logic is a human invention that approximates something in the real world. It's not ideal. That this instrument can lead to paradoxes only tells you that this tool is flawed and you should be careful with your recursions.

>Logically there shouldn't be paradoxes

Formal logic is a human invention that approximates something in the real world. It's not ideal. That this instrument can lead to paradoxes only tells you that this tool is flawed and you should be careful with your recursions.

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