1:00 p.m. Daniel Shira - "Groebner Bases"; advised by Susan Cooper

1:20 p.m. Vijay Shah - "Hilbert Spaces and their Applications"; advised by Indranil SenGupta

1:40 p.m. Anuj Teotia - "Chromatic Functions"; advised by Kevin Dilks

2:00 p.m. Alan Hiltner - "The Jordan Curve Theorem"; advised by Josef Dorfmeister

2:20 p.m. Halley Fritze - "Homology Theory: The Importance of the Eilenberg-Steenrod Axioms"; advised by Josef Dorfmeister

]]>Get help studying for your exams: visit **Math In**!

Minard 310, Minard Annex.

8am - 3pm, Saturday, May 5.

Mathematics faculty, lecturers and TAs will be there to help.

]]>ABSTRACT: I'll introduce some classical knot and link invariants, such as crossing number, unknotting number, and linking number. I'll also state some elementary problems which have been open for a very long time. No knowledge is required.

Location: Minard 112

Time: 5pm

Date: Wednesday, May 3.

Bring your family or a friend. The more the merrier.

For more information, or to RSVP, contact

Melanie Milam

Administrative Secretary - NDSU Mathematics

Ph - 701-231-8171

PS: I hope to see you there as this will be my last picnic before I retire.

]]>Abstract: From the perspective of a pure mathematician, I find the concept of surface curvature to be beautiful due to the simplicity in its construction. For Gauss, he showed that the Gaussian curvature of a surface was an intrinsic quantity. This is a very important theorem in differential geometry. Gauss referred to it as, "Theorem egregium", which translates to, "very awesome theorem". For others, antimicrobial peptides help protect our immune system by sending a wide range of antibiotics throughout our body. It has been observed that these AMP's sometimes arrange themselves to form a shape with negative Gaussian curvature which helps target microbial membranes (cool!). In this talk, we will simply explore the ideas behind defining curvature for planar curves and surfaces.

Location: Minard 112

Time: 5pm

Date: Wed 12 April

This one day mini-conference will focus on the most recent developments related to the stochastic processes and their applications in mathematical finance. The goal of this conference is to bring together leading researchers, as well as junior researchers who are interested in the area of stochastic process and its applications in finance. Another goal is to stimulate interest in the subject among applied mathematicians, engineering scientists and actuarialists in order to promote interdisciplinary research.

]]>Abstract: The standard genetic code is the map, according to which almost any organism on our planet translates the information stored in DNA molecules into the building blocks of our cells - proteins. Historically, there was a period when the genetic code was one of the most intriguing and discussed aspects of biology. One of the reasons was that the code presented us with a fascinating puzzle - deciphering the code words that the cell uses to designate amino acids. In my talk I will explain the necessary biologically background, formulate the problem and review some of the historical developments. At the end of the talk I will give the answer to the quotation from the late 50th: "It will be interesting to see how much of the final solution [to the genetic code] will be proposed by mathematicians before the experimentalists find it..."

Location: Minard 112

Date: Wednesday, 5 April

Time: 5pm

**Abstract**: The rich and diverse history of mathematics is both intriguing and engaging. Knowing the history of mathematics helps to humanize the pioneers who developed the subject and gives us a window into the circumstances under which they worked. In this talk, we shall discuss the development of calculus, with a focus on the work of both Isaac Newton and Gottfried Leibniz, and the famous controversy surrounding the dispute between these two giants about who gets credit for the development of calculus.

Location: Minard 302

Date: 30 March

Time: 3pm

**Abstract**: In this talk, I will give a brief introduction to a field known as Category Theory. One hard concept to handle in the beginning of Category Theory is the natural transformation. However, thanks to the Poincare Dual, we have an efficient way to visualize the relations that the natural transformation has with our categorical diagrams known as string diagrams. We shall delve into some basic proofs using string diagrams and importance of string diagrams into other fields of mathematics if time permits. No prior knowledge is needed for coming to this talk.

Location: 302 Minard

Date: 09 March 2017

Time: 3pm

**Abstract**: The continued fraction expansion (CFE) of a real number provides a novel means of representing real numbers as well as efficient methods of (best) approximations of irrational numbers by rational numbers. In my talk last week I focused on the main features of CFE representation. It turns out that, CFE representation can be obtained via action of a map, the Gauss map, which also remedies some drawbacks of ordinary CFE. In this talk I will focus on the Gauss map; exhibit its connection with the CFE representation and investigate its dynamical aspects such as periodic points, transitivity and measure preserving property.

Location: Minard 112

Date: 8 March 2017

Time: 5pm

Even if you've missed a few talks, just come to this one.

]]>Abstract: At first glance these three topics seem to have no relation, however we will show that if you wish to integrate over a surface ∑ then to get a well-defined definition, we must have that ∑ is orientable. The question now becomes, what does it mean for a surface to be orientable? Moreover, what is a surface?Location: Minard 112

Time: 5pmDate: 15 Feb 2017

**Abstract**: The Mandelbrot and Julia set are extremely beautiful objects (you can see some drawings at the Wikipedia page if you never saw them before, just google it). The mathematics behind them is quite involved. However, to understand how these sets can be generated by a computer does not require anything except for the idea how to multiply and add complex numbers. So in my talk I plan to discuss very basic algorithms to generate these sets, and I will illustrate this discussion with some Mathematica code. A sufficient (but not necessary!) prerequisite for this talk is some familiarity with the field of complex numbers. If you never saw complex numbers before, do not worry, I will start by introducing those bits of information that will be important for my talk.

Location: Minard 112

Date: Wednesday, 8 Feb

Time: 5pm

Abstract: A "Macaulay-type" characterization of the Hilbert functions of finite sets of distinct points which are subsets of complete intersections in projective space P^2 can be given. This brings about the proof that the set of Hilbert functions of subsets of complete intersections of type {d_1, d_2} is the same as the set for rectangular complete intersections of the same type. This verifies the Eisenbud-Green-Harris Conjecture in P^2. This talk is based on Susan Cooper's "Subsets of Complete Intersections and the EGH Conjecture" from 2012.

Minard 302

]]>1/f(x) = ∏ (1-2^{-x})(1-3^{-x})(1-5^{-x})(1-7^{-x})...

and used it to give an alternative proof of the fact that there are infinitely many primes. (A prime is a positive integer p divisible by 1 and p, but by no other positive integer.) Euler’s proof uses nothing more than the geometric series formula and factorizations of positive integers. In this talk we will investigate the product formula and explore some of its consequences.

]]>**Abstract**: One of the main focuses of graph theory is the study of invariants of graphs, most of which are integer-valued. The goal of fractional graph theory is to modify these invariants so they can take on non-integer values in a natural way. We will begin with a brief review of graph theory, then discuss how to modify the chromatic number of a graph so it can take on fractional values. No background is required for this talk.

Location: Minard 302

Date: Thursday, 23 March

Time: 3pm

Hope to see you there!

Sincerely,

Melanie Milam

Administrative Secretary - NDSU Mathematics

Abstract: In Calculus, one encounters functions of certain types: continuous, differentiable, k-times differentiable, infinitely many times differentiable and more. It is often shown that there are functions that possess one attribute but not another. For example, f(x)=abs(x) is continuous but not differentiable (at x=0). I will give examples of functions that fit into one but not another category (if they exist?), show how far one can go and illustrate which role such functions play in mathematics.Minard 112

]]>**Wednesday, December 7 – Minard 220 **

9:00 Keith Lehman – “The incompleteness theorem of Kurt Godel: The logical shift in mathematics,” advised by Dr. Friedrich Littmann

9:15 Emily Naylor – “Constructibility and non-constructibility in compass and straightedge constructions,” advised by Dr. Michael Cohen

9:30 Anuj Teotia – “Total coloring in spider graphs,” advised by Dr. Kevin Dilks **Friday, December 9 – Minard 310**

9:00 Patricia Zikmund – “The influence of the calculus reform on cooperative learning in the secondary mathematics classroom,” advised by Dr. William Martin

9:15 Parker Pavlicek – “Kolmogorov complexity and randomness,” advised by Dr. Michael Cohen

9:30 Eric Kubischta – “Prolate spheroidal wave functions,” advised by Dr. Indranil SenGupta **Monday, December 12 – Minard 220 **

8:00 Veronica Waite – “Kuratowski’s closure-complement problem,” advised by Dr. Michael Cohen

8:15 Jacob Schulze – “Matrix functions,” advised by Dr. Davis Cope

8:30 Mi Huynh – “Fuss-Catalan generalizations of well-known Catalan structures,” advised by Dr. Jessica Striker

8:45 Colton Keller – “A Catalan subset of descending plane partitions,” advised by Dr. Jessica Striker

9:00 Rose Jackson – “Constructible numbers and origami,” advised by Dr. Azer Akhmedov

9:15 Michael Kleinsasser – “Spaces of sequences,” advised by Dr. Maria Alfonseca-Cubero

9:30 Aloysia Pfeiffer – “Musical distances and an extension of the uniform triadic motions,” advised by Dr. Jason Boynton

9:45 Alex Baumgarten – “An introduction to the history of Fermat’s last theorem,” advised by Dr. Friedrich Littmann

For those of you unfamiliar with the International Dinner, we like to have a Potluck Dinner once a year with the people of our department. Bring a main dish, side dish or dessert. An old family recipe or ethnic dish from your heritage would be wonderful.

I hope you will put this on your calendar. We usually have a great time with wonderful food. Bring your family or a friend. The Math Dept. supplies all the flatware, dishes, and beverages.

Sincerely,

Melanie Milam

Administrative Secretary - NDSU Mathematics

To RSVP, contact Melanie.

Top competitors are awarded prizes. The winner's name is engraved on the K. N. Rao trophy. The top three competitors will receive scholarships that can be utilized at NDSU. The top five competitors are awarded gift certificates to the NDSU Varsity Mart.

The contest is open to undergraduate students registered at any of the Tri-College institutions (Concordia, MSUM, and NDSU).

]]>ABSTRACT: In 1638, Fermat proposed that every natural number is a sum of at most 3 triangular numbers, 4 square numbers, 5 pentagonal numbers, and more generally, k k-gonal numbers. Fermat implied that he had a proof of this claim although his proof was not found anywhere.

For k=4, the claim was proved by Lagrange in 1770 (i.e. every natural number is a sum of four perfect squares), and for k=3 it was proved by K.F.Gauss in 1796 (Gauss' result was mentioned in Aziz Issaka's talk). Later, in 1813, Cauchy finally proved the theorem in general.

Even in the case of k = 4, this all involves (is related to) a very interesting and rich (modern) mathematics.

Minard 302

Thursday, 17 November

3pm

ABSTRACT: I'll discuss two theorems on pizza. One is about cutting it, the other one is about eating it. Both theorems have been proved by K.F.Gauss.

302 Minard

Wednesday, 16 November

**Abstract**: The n-ary expansion, special cases of which are decimal expansion and binary expansion, and continued fraction expansion are two main representation schemes of (real) numbers widely used in various branches of mathematics. In their original form, both suffer from the deficit of not producing unique representation for some numbers. It turns out that both of these schemes can be expressed in terms of well-studied processes in dynamical systems. I this talk we will provide some important as well as interesting features of these processes and, time permitting, will explore further extensions.

**Location**: 302 Minard**Date**: 09 November**Time**: 5pm

**Abstract**: In this talk, we'll discuss asymptotic expansion, triangular numbers and harmonic series and then will formulate a formula of Ramanujan, described in Ramanujan's Notebook by B.C. Berndt as "somewhat enigmatic" and goes on to say "we cannot find a "natural" method to produce such an asymptotic series.". In 2008 M.Villarino gave a beautiful proof of this amazing formula and then in 2012 M.D. Hirschhorn also gave another proof hoped to be the "natural method" by using certain 11 asymptotic series for the tail of the Riemann Zeta function. After stating the result of Villarino and Hirschorn and I will finally state our result in a recent paper, where we found a general form of these series used by Hirschorn with an explicit formula for its coefficients and with a precise error term.

Location: Minard 302

Time: 3pm

Date: Thursday, 03 November