Textbook question: Can I self-study with Velleman's Calculus?

[Jamesix]

Summary: CALC BOOK QUESTION

Hey I am going to be self studying calc AP BC because my school only offers AB. So I bought from a ton of reddit advice Vellemans Calculus: A rigorous first course, due to the fact where I want a challenge similar to AOPS however more into solving more problems no using analysis. Is this book of quality and would I be able to breeze through the test with hard work and study?

 

[MidgetDwarf]

If you want rigorous calculus but no analysis, then maybe have a look at Courant:Differential and Integral Calculus, or Moise:Calculus. Courant maybe at a higher level but both offer the same. Moises is easier to read. Coursnt does have more challenging problems tho.

 

[Jamesix]

If you want rigorous calculus but no analysis, then maybe have a look at Courant:Differential and Integral Calculus, or Moise:Calculus. Courant maybe at a higher level but both offer the same. Moises is easier to read. Coursnt does have more challenging problems tho.

Well is vellemans book good?

 

[MidgetDwarf]

The books I mentioned with a few others are the gold standard... Both authors are world class mathematicians.

 

[member 587159]

You want rigorous calculus not using calculus? What do you think rigorous calculus is?

 

[TurboDiesel]

Hi Jamesix,

The AoPS Calculus book seems to be what you want? Velleman is a solid text that is proof-oriented but you'd want to make sure you have a way of verifying your solutions.

MIT has its Calculus of a Single Variable course (18 01) on edX split into Calculus 1A, 1B, and 1C. No book needed. Calculus of a single variable is equivalent to Calculus I&II at some other universities.

Hope this helps!

 

[MidgetDwarf]

Hi Jamesix,

The AoPS Calculus book seems to be what you want? Velleman is a solid text that is proof-oriented but you'd want to make sure you have a way of verifying your solutions.

MIT has its Calculus of a Single Variable course (18 01) on edX split into Calculus 1A, 1B, and 1C. No book needed. Calculus of a single variable is equivalent to Calculus I&II at some other universities.

Hope this helps!

The AoPS books are not even near Courant or Moise. They are junk books.

 

[TurboDiesel]

I want a challenge similar to AOPS however more into solving more problems no using analysis

The AoPS books are not even near Courant or Moise.

This is a fair statement.

I read Jamesix as asking for a problem solving oriented book and specifically not an analysis oriented book. AoPS Calculus includes Putnam problems and similar.

I think you interpret it as seeking applied rather than formal? If he has already done AoPS Calculus, I would suggest something similar, assuming Jamesix is still targeting single variable calculus.

 

[MidgetDwarf]

This is a fair statement.

I read Jamesix as asking for a problem solving oriented book and specifically not an analysis oriented book. AoPS Calculus includes Putnam problems and similar.

I think you interpret it as seeking applied rather than formal? If he has already done AoPS Calculus, I would suggest something similar, assuming Jamesix is still targeting single variable calculus.

He claimed to want Rigor..., and Courant and Moise are not analysis oriented books.

 

[TurboDiesel]

I think you interpret it as seeking applied rather than formal?

Rigor . . . not analysis oriented.

Hi MidgetDwarf,

As you seem to agree with my assessment of your interpretation, I will simply point out that you have an small inconsistency in your interpretation of Jamesix's request (see quoted abbreviation of your post).

AoPS is indeed designed to develop deeper mathematical thinking regarding more elementary ideas. If universities, on average, send three students to Putnam, then there are over ~1,000 universities participating. The median score of students is zero.

Successfully completing the consistent AoPS Calculus provides a superior mathematical thinking foundation for a typical student with which to approach 'deeper' maths. Certainly a prodigy could skip calculus with a good analysis text. [Similarly,] At least one AoPS student has gone to Spivak after AoPS Geometry.

"Volume 1 [of Courant] covers a basic course in real analysis . . ." The Mathematical Gazette

Courant's "Introduction to Calculus and Analysis", is further towards analysis than AoPS Calculus, and I believe we can agree on this.

My best,
TurboDiesel

 

[MidgetDwarf]

Hi MidgetDwarf,

As you seem to agree with my assessment of your interpretation, I will simply point out that you have an small inconsistency in your interpretation of Jamesix's request (see quoted abbreviation of your post).

AoPS is indeed designed to develop deeper mathematical thinking regarding more elementary ideas. If universities, on average, send three students to Putnam, then there are over ~1,000 universities participating. The median score of students is zero.

Successfully completing the consistent AoPS Calculus provides a superior mathematical thinking foundation for a typical student with which to approach 'deeper' maths. Certainly a prodigy could skip calculus with a good analysis text. [Similarly,] At least one AoPS student has gone to Spivak after AoPS Geometry.
Courant's "Introduction to Calculus and Analysis", is further towards analysis than AoPS Calculus, and I believe we can agree on this.

My best,
TurboDiesel

AOP teaches tricks not Mathematics... Are you some kind of investor or receive monetary compensation from AOPS? Courant is not analysis but rigorous Calculus, that will serve any mathematics/physics major for there future studies/ career. Have you looked at the problems in Courant?

 

[TurboDiesel]

"Volume 1 [of Courant] covers a basic course in real analysis . . ." The Mathematical Gazette

Courant is not analysis but rigorous Calculus

Sure. . I think it would be very reasonable to quickly go through Moise or Courant after AoPS Calculus. See my below endorsement of a multi-book approach.

AOP teaches tricks not Mathematics

AoPS is designed around the premise that careening through names of maths courses (and stacks of additional concepts) is less important for a mathematical mind than developing mathematical thinking at each particular level attained (and with each concept covered).

AoPS specifically encourages students to work, on their own initiative, through other books on top of its own texts. This multi-book approach is one I endorse, myself.

My recommendation for a person with an AoPS background seeking problem solving in calculus will differ from my recommendation for a person coming back to calculus after some time (with varying degrees of command), which will also differ from my generic calculus recommendation for a normal kid seeing calculus for the first time who has taken normal math prerequisites.

This is getting off topic so I will probably not go further.

 

[MidgetDwarf]

Sure. . I think it would be very reasonable to quickly go through Moise or Courant after AoPS Calculus. See my below endorsement of a multi-book approach.
AoPS is designed around the premise that careening through names of maths courses (and stacks of additional concepts) is less important for a mathematical mind than developing mathematical thinking at each particular level attained (and with each concept covered).

AoPS specifically encourages students to work, on their own initiative, through other books on top of its own texts. This multi-book approach is one I endorse, myself.

My recommendation for a person with an AoPS background seeking problem solving in calculus will differ from my recommendation for a person coming back to calculus after some time (with varying degrees of command), which will also differ from my generic calculus recommendation for a normal kid seeing calculus for the first time who has taken normal math prerequisites.

This is getting off topic so I will probably not go further.

He already has a textbook from his Calculus course, and wants a rigorous calculus book focused on problems. That is what Courant is, but also adding mathematical insights that will be useful for progress in Academia or employment...

I think you are shill.

 

[TurboDiesel]

He already has a textbook from his Calculus course

The information Jamesix provided is not sufficient to support that speculation.

A . . . first course

Jamesix may have taken AB, but it appears that he intends to not do an AB course and instead, to study a full single variable text on his own in preparation for the BC exam (which covers AB material and provides an AB subscore). Jamesix could be in middle school for all we know. Jamesix did purchase Velleman's Calculus, but not for a course he has taken or that he has said he has the option of taking.

Velleman is a solid text that does stick to calculus that is not analysis-style and does build a strong ability in proofs. It appears that Jamesix may have a background in the AoPS curriculum, in which case he is sufficiently prepared for Moise, Apostol, Courant.

Jamesix also is clearly open to purchasing at least one more text. As stated, I suggest AoPS Calculus best matches his stated target of an AoPS-style calculus text rather than an analysis-style text (Spivak, Apostol, Courant).

My best,
TurboDiesel