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the books only cover courses up to 2nd year only. why doesn't it have titles for 3rd year and 4th year level courses?

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- Thread starter Tom1992
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the books only cover courses up to 2nd year only. why doesn't it have titles for 3rd year and 4th year level courses?

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- #3

JasonRox

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the books only cover courses up to 2nd year only. why doesn't it have titles for 3rd year and 4th year level courses?

They do have titles for upper years.

Some of Schaum's outlines are still good. They're very old so some are outdated like the Abstract Algebra.

Overall, I say they're good because they contain complete solutions to problems. For some subjects though, the solutions are from problems that are easy, which has no use.

As for it being a pseudo-textbook, it never claimed to be a textbook or any of the sort. I originally thought there was no use like cyrus, but my professors would take many questions (almost all) from Schaum's Outlines during seminars. I changed my mind since.

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- #5

JasonRox

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No, you couldn't study directly from a Schaum Outline. There is no way unless the professor absolutely sucks at coming up with his own problems. Actually, most of them suck at coming up with problems, so yeah it could work.

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well that's the thing. i don't think professors will bother to spend time to come up with contest-like, deep-thinking questions for their tests. and from what I've seen all of my test questions so far have been very schaum's-like. i have yet to see a test question that requires me to know the proof of any theorem or understand any topic very deeply for that matter. just know the defintions, the theorems (but not the proofs) and how to use them to answer the question. i don't even have to know what the answer to the question actually signifies to get the full point. so far, i could earn fake A+'s by simply being able to do schaum's problems and nothing else.

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The last few times I taught the introductory courses, I've required some introductory Schaum's outlines as inexpensive supplements to the main textbook... to encourage students to do more problems and more self-studying and to see an outline of the subject from another source.

The outlines are certainly not perfect... but some of them aren't that bad...especially for the price.

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It has very little calculus ,and concentrate more on basic ideas.

My gut feeling is many students like it.

It will not help you to excell in the subject.

But to quickly grasp with various concepts is excellent for.

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mathwonk

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in the past they used to be pretty good. but a few years ago i used them as a problem supplement in honors calc and was very disappoinhted as they seem to have gotten much easier and therefore much less useful.

they are bigger and heavier and fatter and have more pictures but are less useful. this is in line with the decline of all US textbooks in math except top level ones.

but it cannotpossibly hurt you to work asmany problems as possible.

when i was in college i flunked out as a sophomore and worked a year in a factory and came back and jumped right into a diff eq course for which i ahd forgotten all the background. i got a schaums and worked on it hard and soon aced the course. Indeed i got the highest exam score in the class, but i also used other sources for theorems and proofs.

they are bigger and heavier and fatter and have more pictures but are less useful. this is in line with the decline of all US textbooks in math except top level ones.

but it cannotpossibly hurt you to work asmany problems as possible.

when i was in college i flunked out as a sophomore and worked a year in a factory and came back and jumped right into a diff eq course for which i ahd forgotten all the background. i got a schaums and worked on it hard and soon aced the course. Indeed i got the highest exam score in the class, but i also used other sources for theorems and proofs.

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I picked up schaum's outline for calculus in the hopes of getting in some good studying in for a final exam. I didn't even check it out(edit: woops duh, I forgot to say that I went to the library to pick it up and decided to not even check it out... lol). It seemed to focus way too much on plugging and chugging and didn't get down to business with the ideas behind the calculations. It might be good for extra problems and stuff, but I wouldn't say its good for studying. Maybe different outlines differ in the quality of their content, I am not sure.

edit: What I would suggest from what I have seen of the schaum's outline for calculus is to make sure you have your regular textbook with you. Maybe go over your textbook materials once to get the whole picture, and then towards the end of your studying you could use schaum's as a quick refresher to pull everything together.

In the end I would say that they fit into the role of extra practice problems with an attached solutions manual. I can't see why they would ever be neccessary.

edit: What I would suggest from what I have seen of the schaum's outline for calculus is to make sure you have your regular textbook with you. Maybe go over your textbook materials once to get the whole picture, and then towards the end of your studying you could use schaum's as a quick refresher to pull everything together.

In the end I would say that they fit into the role of extra practice problems with an attached solutions manual. I can't see why they would ever be neccessary.

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But overall most Schaum's outlines are good, even though textbooks usually are better, they cost about 10 times more and are not always 10 times better :)

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JasonRox

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It seemed to focus way too much on plugging and chugging and didn't get down to business with the ideas behind the calculations.

That's the whole purpose of the book.

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morphism

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Didn't you say you aren't in university yet?well that's the thing. i don't think professors will bother to spend time to come up with contest-like, deep-thinking questions for their tests. and from what I've seen all of my test questions so far have been very schaum's-like. i have yet to see a test question that requires me to know the proof of any theorem or understand any topic very deeply for that matter.

The fact of the matter is: depending on what school you go to and how tough the courses you take are, tests can be anything but trivial.

Personally I don't own a single Schaum's outline - yet.

- #17

JasonRox

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The fact of the matter is: depending on what school you go to and how tough the courses you take are, tests can be anything but trivial.

Yeah, maybe after 4th year.

I've looked on tests of other schools and they seem trivial to me. Not easy, but if you studied, you most likely came across it.

I wouldn't solely depend on Schaum's Outlines like I mentionned earlier, but there is no doubt it can help a student who has no idea what's going on make a good attempt at passing the course. This is so because it teaches the plug-and-chug way of doing things.

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That's the whole purpose of the book.

Yea, I went to the library expecting something different.

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mathwonk

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Try these freshmnan calc tests on for size:

2300H, test 2, smith, Fall 2000 Name:

(25)I. (i) Give the limit definition of the derivative f’(a).

(ii) Give the neighborhood definition: limx-->a f(x) = L if and only if:

(iii) Give the explicit definition (using epsilon, delta, M, N as appropriate):

limx-->+inf f(x) = L (where L is a real number) if and only if:

(iv) Give the explicit definition: limx-->a+ f(x) = -inf, if and only if:

(v) State the intermediate value theorem:

(20)II. True or False?

(i) If f is continuous on (a,b), f is globally bounded there.

(ii) If g is continuous on (-inf,+inf), g is locally bounded at each point.

(iii) f(x) = 1/x is globally bounded on [1,2].

(iv) g(x) = cos(1/x) is globally bounded on (0,1).

(v) If both one sided limits limx-->a+ f(x) and limx-->a- f(x) exist, then limx-->a f(x) also exists.

(30)III. Find the limits, or if they do not exist, say so. A limit is considered to “exist” if it equals either a finite real number or +inf or -inf.

(i) If [x] = the greatest integer not greater than x, limx-->0- [x] = ?

(ii) If g(x) = xcos(1/x), then limx-->0 g(x) = ?

(iii) limx-->(-5)(x^2-25)/(x+5)= ?

(iv) limx-->2+ (x-3)/(x^2-4) = ?

(v) limx-->+inf (cos(1+x^3))/x = ?

(vi) limx-->0 (x^2+x)/(4x-sin(x)) = ?

(10)IV. Prove there is a real number x such that x^3 + x - 9 = 0. If you use any big theorems, explain why they apply to this situation.

(15)V. Either: prove the “power rule” that if f is differentiable at a, then so is f^n for every natural number n,

Or: prove that sin’(x) = cos(x), (assuming the basic trig limits and the trig addition formulas).

EXTRA: Either prove (5) a differentiable function is continuous,

or (10) a locally bounded function on [0,1], is globally bounded.

2310H Test 2 Fall 2004, Smith NAME:

no calculators, good luck! (use the backs)

1. (a) Define "Lipschitz continuity" for a function f on an interval I.

(b) State a criterion for recognizing Lipschitz continuity in the case of a differentiable function f on an interval I.

(c) Determine which of the following functions is or is not Lipschitz continuous, and explain briefly why in each case.

(i) The function is f(x) = x1/3, on the interval (0, ).

(ii) The function is G(x) = indefinite integral of [t], on the interval [0,10], (where [t] = "the greatest integer not greater than t", i.e. [t] = 0 for t in [0,1), [t] = 1 for t in [1,2), [t] = 2 for t in [2,3), etc....[t] = 9 for t in [9,10), [10] = 10.)

(iii) The function is h(x) = x + cos(x) on the interval (- , ).

2. (i) State the "fundamental theorem of calculus", i.e. state the key properties of the indefinite integral function G(x) = indefinite integral of f from a to x, associated to an integrable function f on a closed bounded interval [a,b]. You may assume f is continuous everywhere on [a,b] if you wish.

(ii) Explain carefully why the definite integral of f from a to b, of a continuous function f, equals H(b)-H(a), whenever H is any "antiderivative" of f, i.e. whenever H'(x) = f(x) for all x in [a,b]. Justify the use of any theorems to which you appeal by verifying their hypotheses.

(iii) Is there a differentiable function G(x) with G'(x) = cos(1/[1+x^4])?

If so, give one, if not say why not.

3. Let S be the solid obtained by revolving the graph of y = e^x around the x axis between x=0 and x=3. Define the moving volume function V(x) = that part of the volume of S lying between 0 and x. (draw a picture.)

(i) What is dV/dx = ?

(ii) Write an integral for the volume of S, and compute that volume.

4. Consider a pyramid of height H, with base a square of side B. Define a moving volume function V(x) = that part of the volume of the pyramid lying between the top of the pyramid, and a plane which is parallel to the base and at a distance x from the top.

(i) Find the derivative dV/dx. [Hint: Use similarity.]

(ii) Find the volume V(H).

(iii) Make a conjecture about the volume of a pyramid of height H with base of any planar shape whatsoever, and base area B.

EXTRA: Either: Prove the FTC. from part 2(i), you may draw pictures and assume your f is monotone and continuous if you like.

Or: ask and answer your own question.

- #20

mathwonk

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Heres another one from the same Fall semester freshman course (and not our Spivak course!):

2310H test 4, Fall 2004, Smith NAME_____________

Do any 4. Say which four to grade.

1. (i) Define what it means, (in terms of “epsilon”), for a sequence {sn} of real numbers to converge to a real limit L.

(ii) [Recall that a lower bound for a sequence {sn}, n > 0, is a number K such that for every n>0, we have sn at least K; and that a greatest lower bound for {sn}, is a lower bound such that no larger number is a lower bound.]

Assuming that {sn} is a weakly monotone decreasing sequence of reals, and that L is a greatest lower bound for {sn}, prove {sn} converges to L.

2.(i) Use an appropriate comparison test for series with positive terms to verify the series for e^x: 1 + x + x^2/2! + x^3/3! + .... , converges absolutely for any fixed x.

(ii) How close to the limit e is the partial sum

1 + 1 + 1/2 + 1/3! + ....+ 1/(10)! ? (Give an explicit estimate for the error, by estimating the size of the omitted terms).

3. Compute the arclength between x = 1 and x=2, of the curve with equation y = (1/8)x^4 + (1/4)x -2. (Show all steps.)

4. Consider a hemisphere of radius r, as generated by revolving the quarter circle x^2 + y^2 = r^2, with x,y at least 0, around the y axis, and derive the area formula A = 2πr^2 for a hemisphere.

5. Compute the antiderivatives:

(i) G' = xsin(x), G = ?

(ii) G' = ln(x). G =?

(iii) G' = arcsin(x), G = ?

(iv) G' = tan^3(x), G = ?

Extra: If a sequence {fn} of continuous functions on [a,b] converge in the sup norm to a continuous function f, then prove the indefinite integrals of the fn also converge in the sup norm to the indefinite integral of f.

- #21

JasonRox

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Those look like good tests to me.

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Then again, im not a math major and its been a longgg time since I did that kind of math. I think I would do very bad on those exams. lol.

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JasonRox

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I actually added all the Finals from 1998 to 2001.

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Do any 4. Say which four to grade.

I love it when teachers do this!

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mathwonk

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