Studying Share self-studying mathematics tips

[symbolipoint]

mathwonk, you have the right ethics in post #200, but when publishers push websites and optical information discs onto the product(a textbook) and push the price way up, something is wrong.

 

[XGWManque]

If you're completely on your own and not in any classes relevant to pure mathematics, then send me a message. I might be able to help. This goes for everybody reading this.

You are probably not going to see this, given that you haven't been active for a while-from what I can tell-but if the offer is on the table, let me know.

 

[0kelvin]

I have decided to learn calculus, linear algebra, numerical methods, all by myself. I did fail all those at university multiple times. So many times that I've lost count.

What I am doing is writing a wiki site. The first thing that I decided to do was to follow intuition and to have as many connections with geometry as possible. If something can be related to physics, statistics, experimental physics, I do it. If some concept from linear algebra can be mentioned to explain something about calculus, I do it. Now people often criticize textbooks for training monkeys by giving rules, applying in exercises and not really teaching the core concepts. Whenever possible I include proofs. If I found the proof online, give credits.

For now I'm not following the same order of a textbook. I'm doing like this. Define a function for one and multiple variables. Write the definition of a limit for one variable and mention that the same idea can be applied to two variables. Then the following page extends it to multiple variables.

If there are mistakes that happen very often I mention them through the text. There are pages dedicated to listing all possible mistakes regarding algebra, limits, derivatives, misconceptions, so on. I even created a page dedicated to listing mistakes regarding grammar that I often make. For ex: if there is a misconception about functions and I can show it with a graph that is intentionally wrong, I show the wrong graph and explain what is wrong with it.

At first I thought that It'd be more or less like a textbook, with examples on the same pages as theory. But the with formatting style of a wiki I decided to split into separated pages. Typing words is 4x faster than typing latex.

My plan is not to cover everything, but at least the core that is shared between engineering, astronomy, computer science, etc.

 

[newbie1127]

I have been self studying for sometime now, ever since Corona hit, our university assigned video call classes were poor quality and less engaging.

One day i started reading out of the reference book and found the language (which i used to think was complex) to be simple. my strategy to self study is very plain

i study with a combination of video lectures + reference book:-
1. I start by getting the outline details of the topic either from the books or the internet, just a short summary of everything i am about to learn.

2. Then, i start watching the lecture and as the professor is going through the concepts, i write my notes that i think are important. (in the beginning i used to write everything, with time i learned how to take notes)

3. Some concepts are going to be complex, and require some contemplation before moving on. so, sometimes i take my time with some things, while othertimes, its plain.

4. After sometime i revisit all the topics i have learned and go over them

5. After revision, i take tests to gauge my grasp on a certain subject

In my experience :

Most of the problems occur at the beginning whether it is the mental challenge of studying alone, the exhausion, the lack of self descipline, lack of experience or even, not knowing how to make notes.
there is no shortage of problems when it comes to self studying but one thing I've learned is if you're consistent and willing, most of those problems go away as soon as you find there is a problem and you get freedom to study whatever you want whenever you want and be more efficient.

Conclusion :

if you have a choice i'd say do what works for you, no need to change whatever has gotten you this far.
or your performance might take a hit.
On the other hand if you're a control freak or like things to be efficient go for it.

good luck

 

[0kelvin]

http://appliedscience.byethost7.com/index.php/Main_Page This is what I'm doing. I'm writing a lot because that's how it works. To explain concepts with words is how I approach it. I've found that once you have the concept, calculations are the easiest part. This is the complete opposite of secondary school, where teachers do repetition of calculations without giving proofs. Some proofs are not feasible because they require number theory, analysis and such. But there is so much emphasis put on mechanical calculations that almost everyone is "spoiled", being unable to see the reason of the calculation in the first place.

For example: at school teachers just tell you that to solve a linear system you can divide everything by two if every constant is a multiple of two. Then people memorize this rule without knowing what concept is behind it. I've seen an admission exam with commented solutions and one comment was that some people take an equation of a function and solve it by dividing everything by 2 or 3 if that's the case. Ok. But when it comes to plot the graph of the quadratic equation, they plot the equation after dividing everything by 2. Which means that people are memorizing rules without knowing what they are doing.

I'm doing much more progress studying like this than attending classes. The problem with classes is that either the teacher spends a lot of time answering questions from other people or the opposite, the teacher doesn't spend a lot of time explaining the concept and you are left behind.

 

[newbie1127]

http://appliedscience.byethost7.com/index.php/Main_Page This is what I'm doing. I'm writing a lot because that's how it works. To explain concepts with words is how I approach it. I've found that once you have the concept, calculations are the easiest part. This is the complete opposite of secondary school, where teachers do repetition of calculations without giving proofs. Some proofs are not feasible because they require number theory, analysis and such. But there is so much emphasis put on mechanical calculations that almost everyone is "spoiled", being unable to see the reason of the calculation in the first place.

For example: at school teachers just tell you that to solve a linear system you can divide everything by two if every constant is a multiple of two. Then people memorize this rule without knowing what concept is behind it. I've seen an admission exam with commented solutions and one comment was that some people take an equation of a function and solve it by dividing everything by 2 or 3 if that's the case. Ok. But when it comes to plot the graph of the quadratic equation, they plot the equation after dividing everything by 2. Which means that people are memorizing rules without knowing what they are doing.

I'm doing much more progress studying like this than attending classes. The problem with classes is that either the teacher spends a lot of time answering questions from other people or the opposite, the teacher doesn't spend a lot of time explaining the concept and you are left behind.

View attachment 300575

Hey,
Could you please tell me what that website is in the picture, I've been looking for good sources to understand calculus and in the picture everything about it seems to be laid out in a nice list.

 

[0kelvin]

Hey,
Could you please tell me what that website is in the picture, I've been looking for good sources to understand calculus and in the picture everything about it seems to be laid out in a nice list.

the link is in the message, the first line. I wrote it.

 

[MidgetDwarf]

I use Understanding Analysis, by Stephen Abbot, because Rudin's book is too difficult to read. I found Understanding Analysis is thoroughly explained. It is an introduction to analysis, so the book does not contain the concept of metric space and Euclidean N-space. Self-studying is extremely time-consuming. It costs me 7 months to learn 7 chapters.

But I am sure those 7 months were time well spent. Moreover, you essentially covered about two analysis classes, give or take. Provided you did most of the problems without looking at the solutions.

Have a look at Apostol's Analysis after. Or if Apostol is too hard, have a look at Bartle: Elements of Analysis.

 

[0kelvin]

Bear in mind that courses often skip chapters and a lot of details.

 

[0kelvin]

I wouldn't recommend doing what I'm doing with my wiki. It takes so much time to write and draw graphs by hand that it's extremely inefficient if you think on good grades.

The current state of my wiki is pre-calculus up to critical points for multivariable functions. I skipped integration for now. It also has introduction to computing with the C language.