Calculus l, ll, and lll

nycmathdad

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Why do most teachers and students agree that Calculus 2 is harder than 1 and 3?
 

skeeter

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Do you have any credible, documented evidence of this assertion, or is this just a purely anecdotal statement based on your personal interaction with calculus students who have completed all three courses and their respective instructors?
 

R.M.

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In my own personal experience, I found calculus 2 to be the most difficult of the three courses, but not 100% due to the content. Yes, the content can be pretty tough (volumes of revolution and infinite series still make me shudder), but in my case there were other factors. I had an excellent professor for calc 1, a pretty good professor for calc 3, and a train-wreck experience for calc 2. The calc 2 course I took was a team-taught hybrid lecture/computer course that wasn't properly developed (it was the mid-90's, and there was a lot of this mindset: oh look, there's computer software, let's use it and assume that the students will figure it out!!!). Looking back, I should have dropped that and taken a more traditional section, but I survived. It did force me to become more self-reliant and I learned a lot about how to (and how NOT to) teach one's self.
 

nycmathdad

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Do you have any credible, documented evidence of this assertion, or is this just a purely anecdotal statement based on your personal interaction with calculus students who have completed all three courses and their respective instructors?
 

nycmathdad

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In my own personal experience, I found calculus 2 to be the most difficult of the three courses, but not 100% due to the content. Yes, the content can be pretty tough (volumes of revolution and infinite series still make me shudder), but in my case there were other factors. I had an excellent professor for calc 1, a pretty good professor for calc 3, and a train-wreck experience for calc 2. The calc 2 course I took was a team-taught hybrid lecture/computer course that wasn't properly developed (it was the mid-90's, and there was a lot of this mindset: oh look, there's computer software, let's use it and assume that the students will figure it out!!!). Looking back, I should have dropped that and taken a more traditional section, but I survived. It did force me to become more self-reliant and I learned a lot about how to (and how NOT to) teach one's self.
I never took Calculus 1, 2, or 3. I was a Sociology major. I did take Precalculus as an elective course and got an A minus in the Spring 1993 semester. In my opinion, Professor Leonard on You Tube is the best math teacher online.

I am currently learning Calculus 1 just for fun. I am watching his video lectures and find the course not so bad (for now). Professor Leonard uploaded an entire Calculus 1, 2, and 3 course for anyone wishing to learn Calculus the right way.

Of course, Calculus 1, 2, and 3 is a walk in the park compared to Advanced Calculus, which I never plan to learn. It is insanely hard. Professor Leonard does not teach Advanced Calculus. In any case, go check out his video lectures recorded in actual class time. Yes, the students are present.
 

jonah2.0

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Beer soaked ramblings follow.
... In any case, go check out his video lectures recorded in actual class time...
I'll tell you what, go check out his video lectures yourself and try to learn something from them.
 

Jomo

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I never took Calculus 1, 2, or 3. I was a Sociology major. I did take Precalculus as an elective course and got an A minus in the Spring 1993 semester. In my opinion, Professor Leonard on You Tube is the best math teacher online.

I am currently learning Calculus 1 just for fun. I am watching his video lectures and find the course not so bad (for now). Professor Leonard uploaded an entire Calculus 1, 2, and 3 course for anyone wishing to learn Calculus the right way.

Of course, Calculus 1, 2, and 3 is a walk in the park compared to Advanced Calculus, which I never plan to learn. It is insanely hard. Professor Leonard does not teach Advanced Calculus. In any case, go check out his video lectures recorded in actual class time. Yes, the students are present.
I never took Calculus 1, 2, or 3. I was a Sociology major. I did take Precalculus as an elective course and got an A minus in the Spring 1993 semester. In my opinion, Professor Leonard on You Tube is the best math teacher online.
What on Earth do all does have in common, especially about Leonard on youtube?

I am currently learning Calculus 1 just for fun.
Did you think that maybe learning arithmetic before Calculus might be beneficial??

Of course, Calculus 1, 2, and 3 is a walk in the park compared to Advanced Calculus, which I never plan to learn. It is insanely hard.
Of the four courses that you mentioned I think that you studied none of them. Can you explain how you then can rate them in terms of difficulty?
Advanced Calculus was not hard at all in my opinion. I felt that it was just as easy as the rest of my other courses that I studied as an undergraduate.


Here is my response to your original question. Which calculus course is hardest? It depends on the particular student and what is going on in their life. I was allowed to take linear algebra along with calculus 3. I absolutely loved the abstractness of linear algebra and put all my energy into learning the beginning of this beautiful subject that I put very little energy into calculus 3. Yes, I earned my A in calculus 3 but it was harder for me because the energy level to learn it just wasn't there.
 

nycmathdad

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I never took Calculus 1, 2, or 3. I was a Sociology major. I did take Precalculus as an elective course and got an A minus in the Spring 1993 semester. In my opinion, Professor Leonard on You Tube is the best math teacher online.
What on Earth do all does have in common, especially about Leonard on youtube?

I am currently learning Calculus 1 just for fun.
Did you think that maybe learning arithmetic before Calculus might be beneficial??

Of course, Calculus 1, 2, and 3 is a walk in the park compared to Advanced Calculus, which I never plan to learn. It is insanely hard.
Of the four courses that you mentioned I think that you studied none of them. Can you explain how you then can rate them in terms of difficulty?
Advanced Calculus was not hard at all in my opinion. I felt that it was just as easy as the rest of my other courses that I studied as an undergraduate.


Here is my response to your original question. Which calculus course is hardest? It depends on the particular student and what is going on in their life. I was allowed to take linear algebra along with calculus 3. I absolutely loved the abstractness of linear algebra and put all my energy into learning the beginning of this beautiful subject that I put very little energy into calculus 3. Yes, I earned my A in calculus 3 but it was harder for me because the energy level to learn it just wasn't there.
Why do you like the abstract part of linear algebra?
 

JeffM

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The hardest course I took in math at the college level was abstract algebra. I suspect it is what separates mathematicians from normal people.

There were perhaps a dozen people in that class. As I recollect, there was one A for a guy who took to it like a duck to water, my B, to achieve which I had to work hard, and a bunch of C’s ov varying degrees. I think it was a required course for education majors who wanted to teach math; they were by and large bemused. Calculus was a breeze compared to abstract algebra because calculus involves a small number of concepts; all the rest is technique.
 

Jomo

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The hardest course I took in math at the college level was abstract algebra. I suspect it is what separates mathematicians from normal people.
I take that personally even if I am not a mathematician!

Abstract Algebra for math ed majors? Funny!
 

JeffM

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I take that personally even if I am not a mathematician!

Abstract Algebra for math ed majors? Funny!
It proved to me that I had not a single mathematician’s bone in my body. Studying history was the right academic field for me: what counts as evidence and how much weight will it bear were things I had an intuition for,

I have no idea what drugs they take in schools of education. When I took Abstract Algebra, it was the heyday of the New Math: quite possibly, Timothy Leary was an advisor back then.
 

nycmathdad

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It proved to me that I had not a single mathematician’s bone in my body. Studying history was the right academic field for me: what counts as evidence and how much weight will it bear were things I had an intuition for,

I have no idea what drugs they take in schools of education. When I took Abstract Algebra, it was the heyday of the New Math: quite possibly, Timothy Leary was an advisor back then.
You majored in history? I thought you had a math degree. I majored in sociology but always had an interest in mathematics.
 

JeffM

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You majored in history? I thought you had a math degree. I majored in sociology but always had an interest in mathematics.
I went to secondary schools that stressed mathematics and language to the almost total exclusion of anything else except the physical sciences. Then I went to Columbia, which loathed specialization in undergraduate education but had an incredible history department. Analysis was ugly, and abstract algebra was hard, and I like history.
 

HallsofIvy

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I am inclined to agree that Calculus 2 is the hard of the sequence. It typically includes "methods of integr0ation", just a jumble of unrelated methods that had to be memorized.
 

nycmathdad

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I went to secondary schools that stressed mathematics and language to the almost total exclusion of anything else except the physical sciences. Then I went to Columbia, which loathed specialization in undergraduate education but had an incredible history department. Analysis was ugly, and abstract algebra was hard, and I like history.
So, did you major in math or history? I heard about abstract algebra aka modern algebra. Thank God I never have to take so a course. What's analysis? Proofs?
 

nycmathdad

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I am inclined to agree that Calculus 2 is the hard of the sequence. It typically includes "methods of integr0ation", just a jumble of unrelated methods that had to be memorized.
Calculus 2 is harder than 1 and 3. I must also say that, according to students, calculus 3 is no walk in the park. However, Advanced Calculus is WAY HARDER than the regular calculus sequence. What are your thoughts on Advanced Calculus?

Here is lecture 1 by James Cook

 

jonah2.0

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JeffM

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So, did you major in math or history? I heard about abstract algebra aka modern algebra. Thank God I never have to take so a course. What's analysis? Proofs?
Analysis is the formal foundation of the real number system, infinite sequences and series, and calculus.

History major.
 

nycmathdad

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Analysis is the formal foundation of the real number system, infinite sequences and series, and calculus.

History major.
Wow! Impressive. A history major with cool math skills.
 
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