Online TA Profiles
Fabio Mainardi, PhD
OTA ID#: 105597
| Education Experience: |
BSc, Mathematics, Rome, 1998 PhD, Mathematics, Paris 13, 2004 |
|---|---|
| Focus of Study: | I have completed my PhD in pure Mathematics |
| Publications: | 1 article submitted to American Journal of Mathematics |
| Work Experience: | Leiden University
2005-2006 Post-doctoral grant, Mathematics Department. I have been working on my research topic. I have also taught a graduate course. Universite' de Paris 13 2002-2005 Assistant professor of Mathematics and Computer Science |
| Skills & Achievements: | I earned a PhD in mathematics, University of Paris 13.
I have 4 years of teaching experience, in English and French. I am a certified teacher, in Italy. I am a native Italian speaker, I know three languages (Italian, French, English). I am a reviewer for the Mathematical Association of America. |
| Career Interests: | I am currently pursing a Master in Financial Engineering at Columbia University, NY, because
I wish to start a career in that field. |
| Outside Interests: | I like music and poetry |
| Message to Students and/or Parents: |
Learning mathematics is not about memorizing formulas. Students are often surprised when I tell them that definitions are sometimes as difficult as theorems and proofs.
Teaching mathematics is a complex and fascinating process, with an ideal point of equilibrium between abstract formalism and down-to-earth intuition. From a psychological point of view, most people (including myself) need some motivation to go through lengthy, technical details; on the other hand, one should never over-simplify: after all, the true understanding of mathematics is a result of patient work. |
| Postings Answered: | 133 |
| Cumulative OTA Rating: | 4.9/5 What is OTA Rating? |
- Analytic functions. Either f or g is zero. - Let G be a region and let f and g be analytic functions on G such that f(z)g(z)=0 for all z in G. Show that either f=0 or g=0.
- Continuity of a Max Function on [0,1] X [0,1] - Let f(x,y) be a real valued continuous function defined on the unit square [0,1] X [0,1]. Prove g(x)=max{f(x,y) : y in [0,1]} is continuous. --- Can we treat g(x) as a composite function that ...
- Remainders of Euclidean Algorithms - Let b = r_0, r_1, r_2, ... be the successive remainders in the Euclidean Algorithm applied to a and b. Show that every 2 steps reduces the remainder by at least one half. In other words, verify that r ...
- Abelian Groups, Nilradicals and Augmentation Ideals - Let p be a prime and let G be an abelian group of order P^n. Prove that the nilradical of the group ring FpG is the augmentation ideal. Please use the following notion to prove: The augmentation i ...
- Show that the sum of two ideals in a ring is also an ideal in that ring. - Let I and J be two ideals in a ring R. Show that I + J = {a + b : a in I and b in J} is an ideal in R.
- Linear Equations, Midpoints and Distance Between Two Points - 6. Consider the points (4, -1) and (7, 8). (a) Find the midpoint of the line segment with the given endpoints. (b) Find the distance between the points. Give an exact answer (simplified as much as ...
- Determining where a function is continuous, Epsilon-Delta Continuity Problem - Determine where the function f(x) = x + [|x^2|] - [|x|] is continuous I don't understand how to work this problem. Can someone show and explain how to solve this problem in detail? I've asked for ...
- Ring Theorem : Finite Boolean Ring - Let R be a finite Boolean Ring with identity 1≠0. Prove that R≡Z /2Z x Z/2Z x Z/2Z……Z/2Z. See attached file for full problem description.
- Compact Sets and Compact Exhaustions - Definition: Let omega be a domain in C. Then e compact exhaustion {Ek} of omega is 1. Ek are all compact, Ek is contained in Ek+1 for all k 2. Union of Ek=omega 3. Any compact set K contained in o ...
- Splitting Fields - Let E be an extension of F and f(x) be in F[x]. Also, let Φ be an automorphism of E leaving every element of F fixed. Prove that Φ must take a root of f(x) lying in E into a root of f(x) i ...
- Short exact sequence is split over ring - Let R be a subring of a ring S and let 0 -> M -> N -> P -> 0 be a short exact sequence of S-modules. Prove or disprove the following statements: (i) If the sequence is split over S, then it is ...
- Show that a nonzero homomorphism of a simple ring is injective. - Show that a nonzero homomorphism of a simple ring is injective. In particular, a nonzero homomorphism of a field is injective.
- Let F be a finite field of characteristic p. Prove that |F|= p^n for some positive integer n. - Let F be a finite field of characteristic p. Prove that |F|= p^n for some positive integer n.
- Eigenvalues : Stability of fixed points of linear differential systems. - Analyze the stability of the fixed points of linear differential systems. Provide several explicit examples, with graphical illustrations
- Cauchy integral formula - Show that the Cauchy Integral Formula follows from Cauchy's Theorem.
- Ring Theory : Abelian Groups, Nilradicals and Augmentation Ideals - Let p be a prime and let G be an abelian group of order a power of p. Prove that the nilradical of the group ring G is the augmentation ideal.
- Examples of Fourier series and sums of numerical series. - We use the Fourier expansions of certain poynomial functions to compute the sum of some useful numerical series. The formulas are quite general and give, at the end, the Fourier expansion of every p ...
- Irreducible Elements, Additive Abelian Groups, Quotient Rings and Chinese Remainder Theorem - Please see the attached file for the fully formatted problems.
- Connected Annulus - Prove the annulus A={z in (the set)R^2 : r <= |z| <= R} is connected. Is it sufficient to show that the annulus is homomorphic to the circle, and then since circle is connected, so is the annulus ...
- Polynomials, Homomorphisms and Quotient Rings - Please see the attached file for the fully formatted problems.
