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I am about 16 years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study mathematics.

I request people to tell me what topics an undergraduate may/must study and the books that you highly recommend (please do not ask me to define an undergraduate).

Background:

1. Single variable calculus from Apostol's book Calculus;

2. I have started IN Herstein's topics in algebra;

3. I have a limited knowledge of linear algebra: I only know what a basis is, a dimension is, a bit of transpose, inverse of a matrix, determinants defined in terms of co-factors, etc., but no more;

4. absolutely elementary point set topology. I think open and closed balls, limit points, compactness, Bolzano-Weirstrass theorem (I may have forgotten this topology bit);

5. binomial coefficients, recursions, bijections;

6. very elementary number theory: divisibility, modular arithmetic, Fermat's little theorem, Euler's phi function, etc.

I asked a similar question (covering less ground than this one) some time back which received no answers and which I deleted. Even if I do not manage to get into a good university, I wish to self-study mathematics. I thanks all those who help me and all those who give me their valuable criticism and advice.

P.S.: Thanks all of you. Time for me to start studying.

I am about $16$ years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study mathematics.

I request people to tell me what topics an undergraduate may/must study and the books that you highly recommend (please do not ask me to define an undergraduate).

Background:

1. Single variable calculus from Apostol's book Calculus;

2. I have started IN Herstein's topics in algebra;

3. I have a limited knowledge of linear algebra: I only know what a basis is, a dimension is, a bit of transpose, inverse of a matrix, determinants defined in terms of co-factors, etc., but no more;

4. absolutely elementary point set topology. I think open and closed balls, limit points, compactness, Bolzano-Weirstrass theorem (I may have forgotten this topology bit);

5. binomial coefficients, recursions, bijections;

6. very elementary number theory: divisibility, modular arithmetic, Fermat's little theorem, Euler's phi function, etc.

I asked a similar question (covering less ground than this one) some time back which received no answers and which I deleted. Even if I do not manage to get into a good university, I wish to self-study mathematics. I thanks all those who help me and all those who give me their valuable criticism and advice.

P.S.: Thanks all of you. Time for me to start studying.

I am about 16 years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study mathematics.

I request people to tell me what topics an undergraduate may/must study and the books that you highly recommend (please do not ask me to define an undergraduate).

Background:

a)Single variable calculus from Apostol's book Calculus

b) I have started IN Herstein's topics in algebra.

c) I have a limited knowledge of linear algebra: I only know what a basis is, a dimension is, a bit of transpose, inverse of a matrix, determinants defined in terms of co-factors etc. but no more.

d) Absolutely elementary point set topology (I think open and closed balls, limit points, compactness, Bolzano-Weirstrass theorem (I may have forgotten this topology bit))

e) Binomial co-efficients, recursions, bijections.

f) Very elementary number theory: divisibility, modular arithmetic, Fermat's little theorem, Euler's phi function, etc.

I asked a similar question (covering less ground than this one) some time back which received no answers and which I deleted. Even if I do not manage to get into a good university, I wish to self-study mathematics. I thanks all those who help me and all those who give me their valuable criticism and advice.

P.S.:Thanks all of you.Time for me to start studying  .

I am about 16 years old and I have just started studying some college mathematics. I may never manage to get into a proper or good university (I do not trust fate) but I want to really study mathematics.

I request people to tell me what topics an undergraduate may/must study and the books that you highly recommend (please do not ask me to define an undergraduate).

Background:

1. Single variable calculus from Apostol's book Calculus;

2. I have started IN Herstein's topics in algebra;

3. I have a limited knowledge of linear algebra: I only know what a basis is, a dimension is, a bit of transpose, inverse of a matrix, determinants defined in terms of co-factors, etc., but no more;

4. absolutely elementary point set topology. I think open and closed balls, limit points, compactness, Bolzano-Weirstrass theorem (I may have forgotten this topology bit);

5. binomial coefficients, recursions, bijections;

6. very elementary number theory: divisibility, modular arithmetic, Fermat's little theorem, Euler's phi function, etc.

I asked a similar question (covering less ground than this one) some time back which received no answers and which I deleted. Even if I do not manage to get into a good university, I wish to self-study mathematics. I thanks all those who help me and all those who give me their valuable criticism and advice.

P.S.: Thanks all of you. Time for me to start studying.