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Math training by James Cubberson - Mon, 16 Jun 2014 18:14:57 EST ID:LFUhSvVn No.14089 Ignore Report Reply Quick Reply
File: 1402956897306.jpg -(81119B / 79.22KB, 634x624) Thumbnail displayed, click image for full size. 81119
I want to be able to solve the problems presented here and similar by the end of the summer, I'm currently at about calculus 2 level engineering math.

How much more do I need to study and what exactly is it that I need to study in order to be able to solve all the problems presented here, I have a lot of time on my hands so I hope my brain is up for it.
>>
Angus Broddleshit - Tue, 17 Jun 2014 21:06:14 EST ID:Dk8yywxc No.14093 Ignore Report Quick Reply
Linear Algebra and Differential Equations, in terms of United States college semesters, normally you would take calculus 3 and then linear algebra and differential equations, so you are two semesters away.

If you go looking around on Amazon or something like that, you should be able to find good textbooks that are readable for independent study for an edge when you take these classes. Personally, I would look for proof based treatments of these subjects to get the most out of it but as an engineering student you may not be required to do much of that. However, if you get a good introductory level linear algebra text for example it should ease you into the proofs and it will help with all your other math classes.
>>
Fanny Podgesick - Wed, 18 Jun 2014 07:07:44 EST ID:LFUhSvVn No.14097 Ignore Report Quick Reply
>>14093
Is #2 a basic linear algebra problem? Or does it already border on functional analysis?
>>
Wesley Supperspear - Sun, 22 Jun 2014 10:28:28 EST ID:8NZnQ0yA No.14112 Ignore Report Quick Reply
1403447308991.png -(70427B / 68.78KB, 1204x732) Thumbnail displayed, click image for full size.
>>14097
The second problem should be provable in a basic linear algebra context since the algebraic structure is just a finite dimensional real vector space without the additional structure that usually allows for functional analysis type study.
>>
Walter Binnerchodge - Thu, 26 Jun 2014 23:26:11 EST ID:HbNSsmiC No.14131 Ignore Report Quick Reply
#3 is an application of mean value and intermediate value theorem from calculus
>>
Shit Nocklestirk - Mon, 30 Jun 2014 03:18:39 EST ID:e1p9nP+4 No.14144 Ignore Report Quick Reply
(1) is single variable calculus.

hint: for the "only if" . assume that both u_n are convergent and the sum is infinite and obtain a contradiction nearly immediately.

the "if" follows from the monotone convergence theorem and the sequence comparison test

(2) is standard linear algebra
hint: diagonalize!!!!!!! eigenvectors are your friend.

(3) is single variable calculus and very simple

hint: see the comment of the person above

(4) is interesting, but doesn't entail and ODE tools or anything
hint: look at Taylor series solutions to the equation to get form a conjecture for the shape of the solutions, then prove conjecture using standard integration techniques. this will be easy for (a) and tricky for (b).


Vector Calc by Rebecca Clobberforth - Sun, 29 Jun 2014 20:48:28 EST ID:wer7kd6a No.14142 Ignore Report Reply Quick Reply
File: 1404089308339.jpg -(134606B / 131.45KB, 1142x297) Thumbnail displayed, click image for full size. 134606
round 3 of trying to type this on a damn forum

Suppose f is any function with continuous second-order partial derivatives such that f(0,0)=0 and (,0) is a critical point of f. Write an expression for the second-degree Taylor polynomial, Q, of f at (0,0)
Q(x,y)=f(a,b)+fx(a,b)(x-a)+fy(a,b)(y-b)+(1/2)fxx(a,b)(x-a)^2+fxy(a,b)(x-a)(y-b)+(1/2)fyy(a,b)(y-b)^2


multiply 0 by Charles Pickman - Sat, 28 Jun 2014 18:22:13 EST ID:tsVlvxIF No.14138 Ignore Report Reply Quick Reply
File: 1403994133366.jpg -(55980B / 54.67KB, 500x383) Thumbnail displayed, click image for full size. 55980
how is it that when you multiply something by 0 the answer is 0? say i have 3 carrots and i multiply the carrots 0 times, would i still have 3 carrots?
>>
Samuel Bluttingham - Sat, 28 Jun 2014 20:05:05 EST ID:8PJ0nVdr No.14139 Ignore Report Quick Reply
http://mathforum.org/library/drmath/sets/select/dm_multiply_zero.html
>>
Bob Bob - Sun, 29 Jun 2014 20:33:18 EST ID:Dk8yywxc No.14141 Ignore Report Quick Reply
>>14138

1*3 = 3 right?

0*3 = (1-1)*3 = 3 - 3 = 0

So you would have 0 carrots.


Sum and diffrences by Phyllis Dringerstore - Thu, 26 Jun 2014 07:28:26 EST ID:aNYGNAvO No.14123 Ignore Report Reply Quick Reply
File: 1403782106366.jpg -(322156B / 314.61KB, 1080x1920) Thumbnail displayed, click image for full size. 322156
Can someone want to help me with c)? I understand it if there are only two parts but i dont know what to do when there are three.
>>
Phyllis Dringerstore - Thu, 26 Jun 2014 07:29:31 EST ID:aNYGNAvO No.14124 Ignore Report Quick Reply
Ops subject was in norwegian
>>
Frederick Punderstet - Thu, 26 Jun 2014 18:26:01 EST ID:lH5+Lnwt No.14125 Ignore Report Quick Reply
Can you give some more context? What are you meant to be doing with them?
>>
Fuck Fellyfoot - Fri, 27 Jun 2014 06:10:08 EST ID:5cShHy72 No.14135 Ignore Report Quick Reply
>>14123
Just apply the rules given in
http://en.wikipedia.org/wiki/Trigonometric_identities#Angle_sum_and_difference_identities
and do the evaluations for Sine and Cosine, as seen in the example.


Squareroots Algebra by Esther Samblechan - Mon, 23 Jun 2014 17:55:42 EST ID:BE8EyBvj No.14115 Ignore Report Reply Quick Reply
File: 1403560542315.jpg -(34751B / 33.94KB, 837x195) Thumbnail displayed, click image for full size. 34751
I'm in calculus and I can't even algebra.
Take a look at this image here. First, I don't understand why they multiplied by (1/x) on top and bottom. I would have never thought to do that to simplify that.

But my main question is in the denominator after it is multiplied by (1/x). What is going on there?!
I thought that if you had a root, like sqrt(1+x), that weren't allowed to go inside and manipulate each term in the root. I thought it was all one part of the root.

Can someone explain the algebra of that highlighted step please?
Thank you
1 posts omitted. Click Reply to view.
>>
DFENS - Tue, 24 Jun 2014 02:50:51 EST ID:S/NbzhXl No.14118 Ignore Report Quick Reply
>>14116
This. Also, you might have not gotten to this point in your calculus course, but when you learn L'Hopitals Rule for evaluating limits this will be easier.
>>
Polly Snodforth - Wed, 25 Jun 2014 15:59:39 EST ID:BE8EyBvj No.14119 Ignore Report Quick Reply
1403726379062.jpg -(5593B / 5.46KB, 198x162) Thumbnail displayed, click image for full size.
>>14116
Ah okay. It makes sense on paper. I still would have never thought of doing this algebra during a test, but we'll see what happens.

Can someone also explain step-by-step on how this result as achieved? (in image)
>>
Polly Snodforth - Wed, 25 Jun 2014 16:07:02 EST ID:BE8EyBvj No.14120 Ignore Report Quick Reply
1403726822062.jpg -(6578B / 6.42KB, 263x87) Thumbnail displayed, click image for full size.
>>14115
Another question regarding this. Where does the (1/x) go?
>>
Clara Nickleham - Wed, 25 Jun 2014 17:09:27 EST ID:8NZnQ0yA No.14121 Ignore Report Quick Reply
1403730567754.jpg -(130982B / 127.91KB, 768x1024) Thumbnail displayed, click image for full size.
>>14119
The cube root of three can be written as (3)^(1/3) and likewise the square root of three can be written as (3)^(1/2). Recall that exponential expressions of real numbers have the property that
(a^x)(a^y)=a^(x+y)
so
(3^(1/3))(3^(1/2))=3^(1/2+1/3)=3^(3/6+2/6)=3^(5/6).

>>14120
The limit of 1/x as x approaches infinity is zero. That's why as the limit is evaluated in your picture, the 1/x term disappears. If you graph the function f(x)=1/x, then you can visualize that as x approaches infinity, f approaches zero, i.e. f has a horizontal asymptote at zero both as x approaches infinity and as x approaches negative infinity. Can you figure out where f(x)=1/x has a vertical asymptote? Otherwise you might roughly think of the situation as when dividing a fixed number by numbers that get successively and arbitrarily larger, then the quotient tends to zero.
>>
Polly Snodforth - Wed, 25 Jun 2014 18:04:54 EST ID:BE8EyBvj No.14122 Ignore Report Quick Reply
>>14121
Thanks, I understand now.
It's just tricky to wrap my head around that when evaluating limits. That you're allowed to just remove things from within that expression, but only if it's a limit. Or I guess it's more like plugging in for X. But you're plugging in Infinity, which just means 1/x -> 0... or something.

But yeah, thanks! This board is mighty helpful it is.


Visually Understanding Math by Shit Blangertere - Tue, 17 Jun 2014 06:57:11 EST ID:RLkenDTl No.14091 Ignore Report Reply Quick Reply
File: 1403002631911.jpg -(499955B / 488.24KB, 1200x780) Thumbnail displayed, click image for full size. 499955
Hi guys,

Wondering if anyone could point me to an introductory level book on Math that teaches primarily by showing how to visualise the math so that I can understand HOW it works (as opposed to just memorising the equations/procedures and accepting that they work).

I'm thinking of going Feynman's Lectures atm, but am wondering if there's something better you guys might recommend.

Again, would like it to start at the very basics if possible.

Thanks and Jesus.
>>
Nigger Grimson - Tue, 17 Jun 2014 15:24:42 EST ID:8PJ0nVdr No.14092 Ignore Report Quick Reply
How introductory do you need?
>>
Django Fairfeather - Tue, 17 Jun 2014 21:13:55 EST ID:Dk8yywxc No.14094 Ignore Report Quick Reply
>>14091

Most well received modern textbooks will have lots of diagrams for more visual learners, the question is what level of material you're looking for. Are you looking for enjoyable math that may not be taught in a course or fundamentals like algebra and calculus?

If you're hardcore you could get a good translation of Euclid's elements, that is about as visual as it gets. I don't have a good recommendation at algebra level, but if you're wanting to learn calculus, Kline's "Calculus: an intuitive and physical approach" is good and doesn't make many assumptions about what you know. Everyone has their own pet favorite calc book though so it may not be helpful for you.
>>
David Pittford - Wed, 18 Jun 2014 04:23:54 EST ID:Gw2IN3ba No.14095 Ignore Report Quick Reply
>Feynman's Lectures

Though these do include chapters on mathematics, they are primarily geared toward teaching physics (you probably already know this). I hear great things about them; and from what I know of Feynman, he probably does a decent job of presenting mathematics in an easily comprehensible way. This reminds me that I need to get around to reading them myself.

However well he presents the mathematical topics, the scope will be narrow - focussing on just the mathematics of physics. But maybe that's all you're looking for. It really depends on which fields of mathematics you wish to understand and your current understanding. You said you wanted to start from the basics, so as >>14094 suggested, try reading Euclid's Elements. You also hinted that you are a visual learner, so maybe this is also a good fit:

http://www.amazon.com/Proofs-without-Words-Exercises-Classroom/dp/0883857006

And then there's always the most recommended resource for math self-teaching: Khan Academy. Obligatory link:

https://www.khanacademy.org/

That's all I got. Good luck!


Math Majors by Shitty Fattits - Wed, 26 Mar 2014 23:09:49 EST ID:xgdLZpNp No.13814 Ignore Report Reply Quick Reply
File: 1395889789436.gif -(1915993B / 1.83MB, 200x200) Thumbnail displayed, click image for full size. 1915993
Howdy, /math/ -- Are there any math majors out there? What do you guys have for jobs? I have plans on becoming a math teacher (secondary level), and I was just wondering if people here did something like that.
16 posts and 1 images omitted. Click Reply to view.
>>
Walter Meddlenore - Wed, 23 Apr 2014 03:59:18 EST ID:kQQi+WA1 No.13932 Ignore Report Quick Reply
I was just going to ask about majoring in math.

What are some other options besides becoming an actuarie?
>>13817
what do you invest in?
>>
Molly Fuckingfuck - Sat, 26 Apr 2014 11:31:37 EST ID:0Lu9efHk No.13940 Ignore Report Quick Reply
>What do you guys have for jobs?

Stevedore
>>
James Clingerhood - Wed, 28 May 2014 22:38:51 EST ID:wtjqoUcj No.14049 Ignore Report Quick Reply
>>13932
My best friend is a math major who, out of school, went to work in ophthalmic optics. Though that's definitely not the norm.
>>
Ernest Gabberman - Wed, 04 Jun 2014 20:14:36 EST ID:E77E4OX5 No.14063 Ignore Report Quick Reply
My advice as a phd student in (pure) math: if you want to make money, don't study pure math (do applied, if anything). An undergrad degree doesn't go into much else other than teaching/actuarial work. If you enjoy/love the subject, then by all means go into it. Just know what you're getting into.
>>
Nathaniel Povingbury - Mon, 16 Jun 2014 18:39:01 EST ID:E8Uxy4mH No.14090 Ignore Report Quick Reply
>>14063
That's not what my math teacher says!


Help? by Xenia Ohiya - Sun, 15 Jun 2014 23:53:53 EST ID:BfGCwHN9 No.14086 Ignore Report Reply Quick Reply
File: 1402890833782.jpg -(587875B / 574.10KB, 1600x1200) Thumbnail displayed, click image for full size. 587875
Markdown amount = $8.19; markdown rate = 22%. Find the original price and reduced price.

How do you set this up?
>>
Thomas Sellerford - Mon, 16 Jun 2014 09:25:44 EST ID:HTgVxC+C No.14087 Ignore Report Quick Reply
Think of it this way, the markdown amount is equal to 22% of the original price. So 8.19=.22x, then divide each side by .22 to get x by itself and you'll get about $37.23. If that's the original price, then the reduced price is $8.19 less, so you do 37.23-8.19 and you get about $29.04. Hope this helps!


Have any of you used this book? Proofs in Math by Betsy Blimmledock - Sat, 31 May 2014 21:41:00 EST ID:8PJ0nVdr No.14054 Ignore Report Reply Quick Reply
File: 1401586860758.jpg -(69255B / 67.63KB, 459x617) Thumbnail displayed, click image for full size. 69255
Would any of you recommend this book as a good introduction to proofs?

http://www.amazon.com/How-Prove-It-Structured-Approach/dp/0521675995
3 posts omitted. Click Reply to view.
>>
Hannah Bingerbury - Fri, 06 Jun 2014 00:39:54 EST ID:SUvMFN4z No.14065 Ignore Report Quick Reply
>>14064

Any reason you're suggesting a calculus textbook?

In my personal opinion Calculus is not a good introductory topic for proofs. It is probably better if the student is comfortable with dealing with formal arguments and then builds from the bottom up, rather than trying to learn fundamental subject matter through its application to more advanced material.
>>
Whitey Huzzleworth - Fri, 06 Jun 2014 01:01:57 EST ID:E77E4OX5 No.14066 Ignore Report Quick Reply
>>14065
Because it's bar-none the best calculus textbook? It starts from the very basic axioms of the real numbers and the proof that the sqrt(2) is irrational and builds up to amazing stuff, and it does so in the most rigorous way possible.

Second, calculus isn't more advanced than the ability to write proofs, at least not anymore.

Most universities offer introduction to logical thinking/proofs courses AFTER the dumbed down plug/chug style calculus course, with this material being relegated to some undergrad intro to analysis course.

Is it easy? No. Will it give you an incredible appreciation for the subject AND the art of proving stuff? Almost surely. Working through all the exercises is essential though, as key stuff (e.g. proof by induction) is buried in there.

For the record, I read it many years ago and my background knowledge was nothing but a spotty knowledge of pre-calc. Now I'm a mathematician. Your mileage may vary.
>>
Molly Worthingwater - Sun, 08 Jun 2014 01:36:49 EST ID:F9AJX/Os No.14067 Ignore Report Quick Reply
>>14066
Yo Spivak, im really happy for you, and imma let you finish... but Apostol wrote one of the best Calculus books of all time

But no seriously, Spivaks Calculus and Apostols Calculus are pretty similar, but I prefer the Apostol text over Spivak. Not sure why, maybe it's because I read it first, but it's a great book for learning calculus (and proofs/logic to a large extent)
>>
Polly Fanway - Sat, 14 Jun 2014 01:33:38 EST ID:Dk8yywxc No.14081 Ignore Report Quick Reply
>>14065

My objection is that real numbers are given axioms without explaining what they are as the completion of the rationals in mathematical logic. It doesn't make sense to me to teach someone something about when they don't understand the fundamentals of what they're learning about.
>>
Fuck Breddlegold - Sun, 15 Jun 2014 22:17:45 EST ID:iDpTdo4u No.14085 Ignore Report Quick Reply
>>14054
Personally, I think it's too slow paced and overly wordy. I would recommend either of these over it
http://www.amazon.com/A-Primer-of-Abstract-Mathematics/dp/0883857081/
http://www.amazon.com/Transition-Advanced-Mathematics-Douglas-Smith/dp/0495562025/
and use this as a supplement for exposure to more interesting proofs
http://www.amazon.com/Conjecture-And-Proof/dp/0883857227/

For a follow up, a good book on mathematical logic would help cement your understanding of what proofs, mathematical theories, models of an axiom system, etc truly mean.


HELP!!! by zian Zeafesh - Sun, 15 Jun 2014 18:49:09 EST ID:BfGCwHN9 No.14083 Ignore Report Reply Quick Reply
File: 1402872549406.jpg -(201038B / 196.33KB, 500x603) Thumbnail displayed, click image for full size. 201038
Sunfresh Bakery makes Italian bread that costs $1.34 per loaf. Past experience shows that 8 percent of the loaves will spoil and have to be discarded. Assuming Sunfresh wants a 45 percent markup based on cost and produces 250 loaves, each loaf of bread should sell for:

I keep going in circles.
>>
Doyle Wentworth - Sun, 15 Jun 2014 20:20:00 EST ID:BfGCwHN9 No.14084 Ignore Report Quick Reply
1402878000545.jpg -(470011B / 459.00KB, 1600x1200) Thumbnail displayed, click image for full size.
1000*.12 = 120 cost
Mark up = 120*1.8 = 216
Selling price per unit = 120+216/960 = $0.35 per pound


Root of a Sequence by Caroline Gunderworth - Sun, 08 Jun 2014 03:16:26 EST ID:m8y4CMIw No.14069 Ignore Report Reply Quick Reply
File: 1402211786270.jpg -(1038985B / 1014.63KB, 790x994) Thumbnail displayed, click image for full size. 1038985
Supposing a sequence An s.t. An>=1 for all n part of the natural numbers and lim An = A, how would one prove the lim root(An) = root(A)?

I tried using the abs(An-a)<epsilon definition but to no avail.
>>
Doris Chaggleman - Sun, 08 Jun 2014 19:39:34 EST ID:MTIV7/tU No.14073 Ignore Report Quick Reply
>>14069
The epsilon method should work. Did you use the fact that the square root function is continuous?
>>
Eugene Nicklefield - Fri, 13 Jun 2014 14:33:27 EST ID:471MpKRU No.14080 Ignore Report Quick Reply
I don't know how rigorous a proof you want, but the first thing that came to me is that this is the limit of the product of sqrt(A) * sqrt(A). There's a property of limits of convergent sequences where lim x*y = (lim x) * (lim y), so maybe you could write A_n as the product of its roots, x_n * x_n, and figure it out form there.


So lost by Devioux Dumatcha - Sun, 08 Jun 2014 16:42:12 EST ID:BfGCwHN9 No.14071 Ignore Report Reply Quick Reply
File: 1402260132614.jpg -(8948B / 8.74KB, 250x188) Thumbnail displayed, click image for full size. 8948
8) Nancy Johnson received a bill for $529.43, dated November 15, with sales terms of 1/14 ROG. The merchandise arrived December 3. Find the cash discount and amount due if the bill was paid December 15.


This is a question on my placement test review/study guide. I have been working on it for over an hour. I am so lost. Can anyone help?
>>
Whitey Worthinggold - Wed, 11 Jun 2014 07:08:30 EST ID:TDWl0A5a No.14079 Ignore Report Quick Reply
If you understand ROG it should be easy

http://www.college-cram.com/study/businessmath/discounts-and-invoices/cash-discounts-using-rog-dating/


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