You are here:
- Home
- Science
- Mathematics
- Advanced Math
Advanced Math/Questions Answered by Expert Clyde Oliver
| Subject | Date Asked |
| recurrences | 5/16/2012 |
| Q: Is there general approach to solve recurrences of form t(n+1)=P( tn ) where P(x) is a ... A: Frankly put, no, there is no such thing at all. The case of a well-behaved linear relation is <a ... | |
| Average depth of binary trees with x% for each new branch growth | 5/3/2012 |
| Q: I've been stuck with this problem for several days now, and as I tend to think longer harder and ... A: This question is quite interesting. Consider that each level of the tree relies only upon the ... | |
| Advanced Linear Algebra | 4/27/2012 |
| Q: #1 Done #2 Despite your admonition, I am seeking some direction on how to approach a proof. #3 ... A: Okay. Let oc denote orthogonal complement, and o denote annihilator. Consider whether (V1)o is the ... | |
| antisymmetric and transitive? | 4/22/2012 |
| Q: I want to ask how to use the matrix? I know about find reflexive and symmetric using the matrix ... A: It is not clear to me the context of this question, so I will do my best to give the most "basic" ... | |
| Advanced Linear Algebra | 4/16/2012 |
| Q: #1 Done #2 Despite your admonition, I am seeking some direction on how to approach a proof. #3 ... A: I am going to assume "sup.o" means orthogonal complement. Given an object f in the dual vector ... | |
| Binomial_Form | 4/4/2012 |
| Q: I have a question regarding the following expression: ... A: Let's be more general. If you have something you think is of the form (X+Y)^n, then it MUST have ... | |
| Binomial | 3/29/2012 |
| Q: I have trouble expanding the expression (a-b)^^n into binomial form. "a" and "b" stand for positive ... A: In order to expand this, you must use the binomial theorem: <pre> < ( n ) (x+y)^n = < ( k ... | |
| Binomial_Form | 3/29/2012 |
| Q: I have a question regarding the following expression: ... A: This is a trinomial - there are three terms added together here. In that case, it would have to be ... | |
| advanced math identities | 3/29/2012 |
| Q: verify the identity: tan (2 inverse tan x)= 2 tan (inverse tan x + inverse tan x^3) A: The best way to verify this identity is to use the formulas for tan(2x) and tan(x+y) on each side of ... | |
| prove convex polygon | 3/28/2012 |
| Q: Prove by strong induction that, for all integers n >= 3, the greatest number of non-crossing ... A: This is true for n=3 because a triangle has no diagonals possible (and for n=3, n-3=0). Take a ... | |
| trigonometric identities | 3/25/2012 |
| Q: ) Here I have problems with this topic.I dont know how to answer the proving identities with the ... A: Generally, to prove complex trigonometric identities, there are a few strategies: 1. Write terms ... | |
| math | 3/21/2012 |
| Q: find an acute angle with meaasure x such that tanx = tan2xtan3xtan4x A: Here, the most important thing is to use <a ... | |
| Iterative Methods | 3/19/2012 |
| Q: Is it true that the Jacobi and Gauss-Seidel methods will always have the same iterative matrix T (as ... A: That is not true. The Jacobi method uses a diagonal matrix and an un-diagonal (zeros on the ... | |
| Volterra Equations | 2/16/2012 |
| Q: I am a math major, but I just recently started taking classes (currently taking analysis). I wanted ... A: A Volterra equation is actually not a PDE, it is an "integral equation." A differential equation ... | |
| math | 1/23/2012 |
| Q: The last 3 digits of some perfect squares are the same and non-zero. What is the smallest possible ... A: There are a few ways to consider this question. The first is easy, but not very insightful - this ... | |
| Trig Identities | 11/21/2011 |
| Q: I've been having some trouble with verifying trig identities. A question I found online that is ... A: The trick is to convert secants to cosines and work backwards (using reversible steps): ... | |
| Fixed point iteration - Contraction theorem | 11/8/2011 |
| Q: Clyde here is the full question, the formulas were correct! Given an initial guess x(0), consider ... A: Well, it's easiest (for me, at least) to think graphically, but the way to do inequalities with e^z ... | |
| Fixed point iteration - Contraction theorem | 11/8/2011 |
| Q: Clyde here is the full question, the formulas were correct! Given an initial guess x(0), consider ... A: Just to be clear - yesterday you did not mention that x* is mean to be a root of f(x). However, you ... | |
| Number Theory | 10/30/2011 |
| Q: I saw this at a math contest website, and it has me stumped: A series of integers A(n) satisfies ... A: What you do is consider the remainder of each expression, upon division by 4. This is called ... | |
| Ski Resort Question | 10/18/2011 |
| Q: I work at a ski resort in marketing, and am really needing a solid answer to a math question. I've ... A: Let's set up variables: C = # of chairs R = # of times the chairs go around in an hour T = # of ... | |
| Matrix | 10/12/2011 |
| Q: Good Afternoon Oliver, I was wondering if you could explain me as to how can one find ... A: The idea will be the same - to re-orient the system so that the system is reflecting through a plane ... | |
| Proposition | 10/8/2011 |
| Q: I need help to answer this question, I am taking mathematics discrete in my distance learning ... A: The fastest way to simplify this proposition is using a truth table - symbolically, you can simplify ... | |
| Math logics | 10/2/2011 |
| Q: Is it true that if A, B, C, and D are nonempty sets, then AxB=CxD if and only if A=C and B=D? I'm ... A: It is true - and it is important that these sets are nonempty. I will go over how you can start from ... | |
| Factorization | 9/22/2011 |
| Q: Please let me know if the below detailed algorithm is a unique way to find factors (i.e. ... A: As far as I can tell, the methods are roughly the same. Both algorithms start with the hope that N ... | |
| Factorization | 9/20/2011 |
| Q: Please let me know if the below detailed algorithm is a unique way to find factors (i.e. ... A: I'm sorry to say that this is a common way of factoring integers. It is very similar to <a ... | |
| Series | 7/3/2011 |
| Q: Oliver, I am studying differential equations on my own. I use books as well as the internet. I work ... A: Let me give you some guidance first - follow up if you need more details. (I hesitate to provide all ... | |
| Limit | 6/29/2011 |
| Q: I have learned Linit theory of math well.but I have a basic question and that is why basically ... A: 1 -- you can if the function is continuous. For more on that topic, look at: ... | |
| Non-prime 7's | 6/27/2011 |
| Q: One of my friends asked me about the square root of 111, and it got me to thinking (when I think ... A: What you've stumbled upon is a part of mathematics called "arithmetic" or, in more modern times, ... | |
| Limit | 6/26/2011 |
| Q: I have learned Linit theory of math well.but I have a basic question and that is why basically ... A: A limit is the question "what does this expression do with numbers near the value in question?" not ... | |
| math | 6/16/2011 |
| Q: Remove the multiples of 2 from the natural numbers,as well as the mutiples of 3,but keep the ... A: This is an interesting question - so let's start with a different question first and work our way up ... | |
| patterns | 6/4/2011 |
| Q: . . . etc. etc. determine the general statement . . . . . ... A: Let me try to give you an example that is different, and walk you through it. Let the sequence ... | |
| patterns | 6/3/2011 |
| Q: . . . etc. etc. determine the general statement . . . . . ... A: Let me try to give you a good overview of various ways to solve - or at least to approach - this ... | |
| Torsion | 6/3/2011 |
| Q: how do you derive the torsion to a curve in terms of r(t)? i.e. where does the following come from ... A: If this is the computation you are making, then you have to make two distinctions: What is |r|' ? ... | |
| Torsion | 6/1/2011 |
| Q: how do you derive the torsion to a curve in terms of r(t)? i.e. where does the following come from ... A: Torsion is a quantity indicating how "fast" the normal vector of the curve is rotating. Assuming for ... | |
| Study of Mathematics | 5/16/2011 |
| Q: Let me start off by offering my apologies if I'm asking this question in the wrong section. What ... A: Well, I'm not sure in which section you would be supposed to ask this question. But here you are, ... | |
| advanced calculus | 5/14/2011 |
| Q: prove that the determinant of any square matrix is a polynomial A: This is not a very well-posed question for several reasons: 1. It is almost certainly homework. ... | |
| markov processes | 5/14/2011 |
| Q: Im doing some revision of markov processes and queueing theory before i start my next uni subject ... A: I can't give you the whole solution to this problem, but let me help you consider how to set up a ... | |
| Exponential Equations involving "e" | 5/4/2011 |
| Q: x+1 3e +1=10 My math 112 teacher gave us a final exam review to take home along with the ... A: I will answer this question, but please consider the fact that this is not "advanced math" in any ... | |
| Statistics and Probability | 5/4/2011 |
| Q: The owners of Superb Coffee want to buy 100 bags of coffee from Great Aroma. They take a sample of ... A: I'm afraid that statistics are not mathematics, and I cannot answer this in terms of some "plug and ... | |
| Arthimetic | 4/15/2011 |
| Q: I read in a book that a number is divisible by 3 if sum of the digits is divisible by 3 . I dont ... A: This is, in fact, true. It is also true for divisibility by 9 (assuming you believe it for 3, ... | |
| Affine Transformations | 4/15/2011 |
| Q: I am struggling with the followingThe transformation f is reflection in the line y=1, and the ... A: It is unclear to me what is the purpose of "g" in this question. I will assume that the map g is ... | |
| The Use of Probability | 4/13/2011 |
| Q: My math class has nearly finished our probability unit, and I honestly hate the subject. Why would ... A: This question is actually somewhat puzzling to me - not puzzling in that the answer is difficult to ... | |
| Sequence to Function | 4/4/2011 |
| Q: Let P(x) be a non-constant polynomial such that P(x^2 + 1) = (P(x))^2 + 1 for all real numbers x and ... A: You have proved that P(x_n) = x_n for all values of n? Then you're done. No two polynomials agree ... | |
| remainder | 3/30/2011 |
| Q: find the remainder when 2^2001 is divided by 2001. ANSWER: The best way to approach this question ... A: To be frank - this is easy and short. It would hardly fill than a couple pages of paper, and ... | |
| Integral using contours and residue thm. | 3/29/2011 |
| Q: Find ∫e^(-x^2)dx from ∞ to - ∞ using contours and residues. A: Although this appears to be a homework question, I will sketch the outline of the computation: Let ... | |
| permutations | 3/22/2011 |
| Q: This question is regarding conjugacy in permutations. The cycle form of P= (135)(24) and S= ... A: This question may be easier to understand if we spend some time playing around with permutations. ... | |
| exponential functions | 3/20/2011 |
| Q: In exponential equations is there one set answer if K in y=ka^x is one? will the line on a graph ... A: Yes, generally speaking the function f(x) = k a^x will have exactly one solution to f(x)=1. There ... | |
| Precalculus - Related Rates | 3/13/2011 |
| Q: A cone is made by cutting a sector of angle (theta) from a circle of radius 1 and gluing the edges ... A: The important thing here is determining what the dimensions of the cone are. In particular, you need ... | |
| remainder | 3/10/2011 |
| Q: find the remainder when 2^2001 is divided by 2001. A: The best way to approach this question is to simply experiment and see what happens. You take ... | |
| Glass Cuboid | 3/5/2011 |
| Q: a glass cuboid has a volume of 500cm^3 and it's sides are xcm and height hcm show that the case is ... A: This is a simple calculus optimization question. I suspect it is homework, in which case I suggest ... | |
Advanced Math
Answers by Expert:
Clyde Oliver
Top Expert on this page
Expertise
I can answer all questions up to, and including, graduate level mathematics. I am more likely to prefer questions beyond the level of calculus. I can answer any questions, from basic elementary number theory like how to prove the first three digits of powers of 2 repeat (they do, with period 100, starting at 8), all the way to advanced mathematics like proving Egorov's theorem or finding phase transitions in random networks.
Experience
I am a PhD educated mathematician working in research at a major university.
Organizations
AMS
Publications
Various research journals of mathematics. Various talks & presentations (some short, some long), about either interesting classical material or about research work.
Education/Credentials
BA mathematics & physics, PhD mathematics from a top 20 US school.
Awards and Honors
Various honors related to grades, various fellowships & scholarships, awards for contributions to mathematics and education at my schools, etc.
Past/Present Clients
In the past, and as my career progresses, I have worked and continue to work as an educator and mentor to students of varying age levels, skill levels, and educational levels.
©2012 About.com, a part of The New York Times Company. All rights reserved.