My Journey With Mathematics

pka said:
harpazo, you have that exactly backward. Mathematics has very little to do with science but applied mathematics does. Like the-cat I did a double major in mathematics and philosophy. Also that way I avoided the dreaded DE course.
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I saw a few minutes of an advanced calculus course on you tube (calculus beyond multivariable calculus aka calculus 3). Most math majors agree it is one of the toughest courses in the math department, harder they say, than algebraic topology.
 
Advanced calculus is an undergraduate course (1st course after high school calculus!) while algebraic topology is a graduate level course. I will not debate this with you but algebraic topology is a more vigorous course then advanced calculus.

I did a MA degree at CUNY (CCNY) and when I asked my advisor what was the difference between a MA and MS degree in math he said that he did not know. That was enough for me to know that there is no difference.
 
harpazo said:
I saw a few minutes of an advanced calculus course on you tube (calculus beyond multivariable calculus aka calculus 3). Most math majors agree it is one of the toughest courses in the math department, harder they say, than algebraic topology.
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Before you take algebraic topology you take one full year of real analysis. Real analysis is a continuation of advanced calculus. RA is much more vigorous then advanced calculus.
Please stop saying that people tell you things when they didn't. Absolutely no one will tell you that they took algebraic topology as an undergraduate
 
I went to a college where math majors needed to have decent talent to survive. Not one of us thought that advanced calculus was hard. Now on the other hand if you go to some other colleges (I'll not say any names but I will say think private colleges) then sure some of their math majors would find advanced calculus difficult.
 
Jomo said:
Advanced calculus is an undergraduate course (1st course after high school calculus!) while algebraic topology is a graduate level course. I will not debate this with you but algebraic topology is a more vigorous course then advanced calculus.

I did a MA degree at CUNY (CCNY) and when I asked my advisor what was the difference between a MA and MS degree in math he said that he did not know. That was enough for me to know that there is no difference.
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This is the first video of an advanced calculus course. This is BEYOND calculus 3 aka multivariable calculus. Check it out.

 
Jomo said:
Before you take algebraic topology you take one full year of real analysis. Real analysis is a continuation of advanced calculus. RA is much more vigorous then advanced calculus.
Please stop saying that people tell you things when they didn't. Absolutely no one will tell you that they took algebraic topology as an undergraduate
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At Lehman College (my former CUNY school) topology is the last course in the B.A. math program or at least that was the case back in the 1990s.
 
Jomo said:
I went to a college where math majors needed to have decent talent to survive. Not one of us thought that advanced calculus was hard. Now on the other hand if you go to some other colleges (I'll not say any names but I will say think private colleges) then sure some of their math majors would find advanced calculus difficult.
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I posted lesson 1 of an advanced calculus course. After just a few minutes, I decided not to study calculus beyond calculus 3. Again, this is not calculus 3. This is beyond, way beyond the normal calculus series. Watch the clip.
 
Actually, the video clip is not really beyond Calculus III it is merely a generalization of the techniques of Calculus III to more general dimensions. Believe it or not once you get to a certain level and have the required knowledge of vector spaces this is actually really fairly standard.

Now, there is "algebra" and there is "Algebra." "algebra" is what you learn in High School and early College semesters. We have the usual real number system and we can set up unknowns and polynomials and Calculus and the like. "Algebra" extends these ideas to more general Mathematical systems, involving groups, rings, and fields which are not necessarily based on the real number system. Topology is sort of an extension to geometry in the sense that we can talk about properties such as compactness and connectedness of a space. Algebraic Topology combines the two so we can, say, be working with things like how to construct a field on the surface of a torus.

Algebraic Topoloy is rather harder (to put it mildly) than Advanced Calculus.

-Dan
 
topsquark said:
Actually, the video clip is not really beyond Calculus III it is merely a generalization of the techniques of Calculus III to more general dimensions. Believe it or not once you get to a certain level and have the required knowledge of vector spaces this is actually really fairly standard.

Now, there is "algebra" and there is "Algebra." "algebra" is what you learn in High School and early College semesters. We have the usual real number system and we can set up unknowns and polynomials and Calculus and the like. "Algebra" extends these ideas to more general Mathematical systems, involving groups, rings, and fields which are not necessarily based on the real number system. Topology is sort of an extension to geometry in the sense that we can talk about properties such as compactness and connectedness of a space. Algebraic Topology combines the two so we can, say, be working with things like how to construct a field on the surface of a torus.

Algebraic Topoloy is rather harder (to put it mildly) than Advanced Calculus.

-Dan
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Thank you for the information. Interesting.
 
You do realize that Topology and Algebraic Topology are not the same course? I have been told by many mathematicians that Algebraic Topology is probably the hardest field in math. Personally I never met anyone who did research in that field.
 
harpazo said:
At Lehman College (my former CUNY school) topology is the last course in the B.A. math program or at least that was the case back in the 1990s.
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There is no last course in a math BA program at Lehman or anywhere.
 
Jomo said:
You do realize that Topology and Algebraic Topology are not the same course? I have been told by many mathematicians that Algebraic Topology is probably the hardest field in math. Personally I never met anyone who did research in that field.
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I recall Soroban (former MHB AND FMH) member telling me the same thing back in 2006.
 
harpazo said:
Check the Lehman College website. I said back in the 1990s.
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I know what you said. In the catalogs it states a sample of courses you can take term by term but one does not need to follow that sample exactly. The only way you could be correct is if the prerequisite for Topology is ALL the math courses that the college offers and I doubt that as one does NOT have to take every course the department offers to graduate! What you are clearly saying is that at Lehman in the 90s after you take Topology you can NOT take any other math course (because Topology is the last course!). That is just absurd to say. You know that no one tells you this stuff but rather you make it up.
 
Jomo said:
I know what you said. In the catalogs it states a sample of courses you can take term by term but one does not need to follow that sample exactly. The only way you could be correct is if the prerequisite for Topology is ALL the math courses that the college offers and I doubt that as one does NOT have to take every course the department offers to graduate! What you are clearly saying is that at Lehman in the 90s after you take Topology you can NOT take any other math course (because Topology is the last course!). That is just absurd to say. You know that no one tells you this stuff but rather you make it up.
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I am not making up anything. This is what a Lehman student majoring in math told me in the 1990s but of course this was long ago, which means I could be wrong. At least I'm humble enough to admit when wrong.
 
A little logic would say that you are incorrect even if a student told you that. How can it be not possible that after you take Topology that the department refuses to allow you to take any other math classes????
 
Jomo said:
A little logic would say that you are incorrect even if a student told you that. How can it be not possible that after you take Topology that the department refuses to allow you to take any other math classes????
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If I recall correctly, the student told me that he had taken 10 math courses before the department allowed him to take topology.
At the time, a student majoring in math needed 44 credits (4 x 11 = 44) to satisfy the requirements for a B. A. or B. S. in Mathematics. I met this guy (forgot him name) in speech class. Back in the 1990s, all students REGARDLESS of major had to take a speech course to graduate from Lehman College plus the CWE or College Writing Exam.
 
I've taken "abstract" at the undergrad level and "modern" at the graduate level, and found that both courses covered the same basic 3 topics: groups, rings, fields. In fact, the graduate course was officially listed as just 'algebra', but the professor referred to it as "modern algebra" occasionally. Long story short, it's another example in mathematics of giving different names to the same thing.
 
That sound amazing but let's assume it is true. A student could have taken a 12th math course AFTER topology as an elective.
 
Jomo said:
That sound amazing but let's assume it is true. A student could have taken a 12th math course AFTER topology as an elective.
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Considering that this took place long ago, and the fact that I will never take topology or ever be a college student again much less a math major, the time has come to move on.
 
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