# Math Colloquium

Each semester, the mathematics department hosts a seminar series for students and faculty.

Experts present recent research findings, giving students a chance to learn about how what they study now applies to the real world. Students have the opportunity to interact with professionals in the field of mathematics, science, and computer science.

### Past Colloquia

**Bibliometrics: Computing with Words **Bibliometrics is the study of statistical and mathematical techniques applied to the analysis of text and documents. This talk gave a general overview of the subject, along with an in-depth exposition of the author’s research on co-citation analysis, a branch of bibliometrics.

The talk concluded with the discussion and demonstration of an online system, AuthorMap, that illustrates the concepts in real-time with a scholarly, substantive dataset, the Arts and Humanities Citation Index.

**Finding Numbers That Are Both Triangular and Square**

The problem of finding triangular square numbers is based on ideas that are more than 2,500 years old. The solution illustrates classic problem solving techniques such as looking for a pattern and solving simpler problems.

This problem also introduces such mathematical topics as Pell’s Equations, continued fractions and their convergents, and recursion.

**How Large a Sample Size Do We Really Need?**This colloquium discussed the basic trade-offs in statistical estimations: the desire to have a high confidence level, a low margin of error, and a small sample size.

This talk answered the common question from decision makers who are planning estimation: How large a sample size do we really need?

**More Graph Theory**This talk described elementary areas of graph theory, including subgraphs, trees, bipartite graphs, and abstract and geometric graphs.

**The Magic of a Square**How can a square be magical? This presentation taught how to create your own magic squares without a wand!

**Intelligent Design versus Evolution**Many feel that certain aspects of intelligent design are at variance with Darwinian evolutionary theory. This talk looked at the theories of intelligent design and evolution and why there are disputes between these two beliefs about how life arose on Earth.

**Mathematics and Religion: The Intersection Is Not Empty**Discussed interesting numbers you meet in the Bible and their special properties, as well as contributions made to mathematics by religious leaders

**The Traveling Salesman Problem and Its Polytope**

Defined the famous traveling salesman problem and explained its importance, linked the problem to the study of polytopes (basically, polygons in more dimensions), and showed results relating data about the traveling salesman polytope to information about its associated problem

**Of Yeast and Men: What Yeast Can Tell Us About Human Biology?**The fungus yeast is studied extensively as a tool to learn about the molecular mechanisms that govern human cells. This talk presented some laboratory findings on yeast genetics.

**Slices of Pi**The number π, the ratio of a circle’s circumference to its diameter, has fascinated people for millennia. This talk discussed the history of π, talked about other places π appears, and described a few ways to calculate its value. Refreshments were served shortly before 3:14:16PM.

**The Anti-Authoritarian Derivative**A certain class of continuous linear functionals called distributions defined on the infinitely differentiable functions on R with compact support was considered. Any integrable function can be associated with one of these so-called generalized functions. After examining the derivative of a distribution, this notion was used to differentiate functions that are not differentiable in the traditional sense.

**Studying a 250-Million-Year-Old Microbe**This presentation described a research project that involves gaining an understanding of the basic biology of a salt-loving microbe that was extracted from a 250-million-year-old salt crystal from a mine in Carlsbad, New Mexico.

**Teaching with Cross Sums**A cross sum is a puzzle shaped like a crossword but with number clues and answers. Attendees discussed both the usefulness of cross sums in introducing the idea of proof to students and several solution techniques that range from simple logic to linear algebra.

**Separation Anxiety? Just Go with the Flow: How Flow Cytometry is Used to Separate Cells in Biotechnology**

Flow cytometry is a technology that enables analysis of multiple properties of cells at a rate of 500–4,000 cells per second. A flow cytometer is able to measure simultaneously the scatter and fluorescence properties of cells as they pass in a fluid stream through a laser interrogation path.

Through a DCED state grant, the Science Department at Cabrini acquired a FACSCalibur flow cytometer and was implementing laboratory assays into the biotechnology curriculum.

This talk outlined the basic steps involved in flow cytometry and showcased some of the work conducted by students enrolled in Theory and Practice in Biotechnology I.

**Thermal De-polymerization**Since the early 20th Century, scientists have been attempting to synthesize fuels from other organic materials. Until recently, none have been successful. A scientist has developed a combination thermal and mechanical process that breaks down virtually any carbon compound into trace elements, solid carbon, pure water, natural gas, and a fuel that is very similar to home heating oil.

The process, in terms of a ratio of energy in compared to energy out, is about 85% efficient. Beyond theory, one full-scale plant is now in operation near St. Louis, Missouri, creating useful compounds from the refuse of a huge poultry-processing plant.

**An Introduction to Graph Theory**This talk covered some introductory graph theory with some simple applications.

**Problem Solving in the Middle School: Using Historical Problems**Problem solving is the number one priority in mathematics in schools. Eighth-grade students at the Armenian Sisters Academy were involved in a project designed to enhance their problem solving skills. Students demonstrated their work. Three types of problems were used:

- General problems from the history of mathematics.
- Problems from a 19th Century American arithmetic text.

**Regression: Theory and Application**Regression is one of the most-used statistical techniques in all fields of research today. There are applications in fields ranging from the physical sciences to the social sciences and education. There are also many different forms of regression, such as multiple regression, logistic regression, and probit models, among others.

This talk introduced the underlying mathematical theory of regression in general and expanded into one application of multiple regression with a model to interpret the results to give those who are familiar with this technique a refresher and those new to this technique an appreciation for the use of this technique in research.

**Solar Activity and Sunspots**Discussion included solar activity and sunspots and, using a special filter, participants took turns looking through a telescope outside to try to observe sunspots.

**The Early History of Computers**

Described the history of calculating devices up to the time of Charles Babbage in the 19th Century

**The Distribution of Decimals**Let x be a real number and (x) be its decimal part so 0 ≤ (x) < 1

This talk described how the values in a particular sequence are distributed and extended the results to other related sequences.

**Look at What we Discovered About Mathematics and Computer Science on Stamps**Discussed a collection of more than 1,000 stamps with mathematical themes

**Codes of Our Life**What do the expiration dates on your credit cards, bar codes, ISBNs, checking accounts, and UPCs have in common? With just elementary school mathematics we can begin to understand some of the mysteries of the high tech codes of our lives.

**Artificial Intelligence and the Genetic Equations**Discussion of artificial intelligence and the connection between it and problem solving with the genetic model as compared to brute force

**Cryptography**Discussed various types of cryptography, along with their uses, history, and other related issues

**Vedic Mathematics**Demonstrated a way of seeing mathematics in a new perspective using the ancient Indian Vedic mathematics laws

**The Logic of Lewis Carroll**Glimpsed into the logic and mind of Lewis Carroll, who viewed logic as a game, using examples from his book and playing a game with logic

**Paradoxes in Probability**Described some well-known and recently publicized unexpected results in probability and statistics, including Simpson’s paradox, the Monty Hall problem, the Hat Puzzle, and Parrondo’s paradox

**An Introduction to Scientific Workplace**Scientific Workplace is a combination of the mathematical typesetting program LaTex and the computer algebra program MAPLE. This talk demonstrated the capabilities of Scientific Workplace and showed how it can be used in upper-level mathematics courses.

**Mathematics in the Movies**A discussion about how mathematics and mathematicians are portrayed in films and stereotypes that exist

**Game Theory and the Old Testament**An overview of game theory and some applications in Biblical conflicts

**Mathematics and Art: Some Connections**Discussion about the paintings of Crockett Johnson, as well as other intersections of mathematics and art

**Why 0 ^{0} is usually 1**In the treatment of L’Hopital’s rule and indeterminate forms given in calculus books, most examples of the indeterminate form 0

^{0}result in an answer of 1. This talk explained why this is so.