CS 173 | Introduction to Computer Science II | Spring 2017 |

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Today |

Stephen Oloo

Visiting Assistant Professor

Kalamazoo College

Kalamazoo, MI

I will introduce projective space and discuss how it is a better setting for doing geometry than our familiar euclidean space. In truth, this discussion will really be an excuse to introduce interesting mathematical ideas such as compactifications and moduli spaces. We may even delve into some algebraic topology.

Palenske 2273:30 PM

All are welcome!

Ursula Whitcher

Associate Editor

American Mathematical Society

Ann Arbor, Michigan

If you have a rubber band and a pegboard, how many polygons can you make that have only one peg in the center? The answer to this question is highly interesting to string theorists, who use shapes like these to write equations for the predicted "extra" dimensions of the universe. We'll talk about the way mathematicians use intuition from string theory to make mathematical discoveries.

Palenske 2273:30 PM

All are welcome!

David A. Reimann

Associate Professor

Albion College

Albion, MI, USA

A degree in mathematics or computer science is excellent preparation for employment in areas such as teaching, actuarial science, software development, engineering, and finance. Come learn about career opportunities awaiting you after graduation.

Palenske 2273:30 PM

All are welcome!

Chris Creighton, '11

Graduate Student

Purdue University

West Lafayette, Indiana

The aim of this talk is to give an introduction to Algebraic Curves, that is, the zero set of some polynomial equation in two variables. We'll mosey through varieties in general and stroll through why the coefficients of the polynomial matter. The path of choice is concepts of nonsingularity and rational functions on the curve. If time, we can go onto the side path of divisors and related topics.

Palenske 2273:30 PM

All are welcome!

Darren Mason

Professor

Albion College

Albion, MI

The current price of Apple stock is $131.74. You are offered a chance to enter into the following agreement:

- If tomorrow Apple stock increases to $133.22, you receive nothing;
- If tomorrow Apple stock decreases to $129.88, you receive $1.12. you receive $1.12.

The above scenario is an example of a financial option called a "put" stock option, which gives the owner the right, but not the obligation, to sell an asset to another person at a particular time (or times) in the future. In the above case, you are guaranteed that you can sell Apple for $131, regardless of stock value. How to fairly price such options, as well as other types of

By the end of this talk you should be able to fairly price the above Apple stock option, as well as understand and price more complicated financial derivatives, within a universe where time discretely ticks by. Palenske 227

3:30 PM

All are welcome!

Robert Messer

Albion College

Albion, Michigan

Wikipedia says, "The Möbius band is a surface with only one side and one edge." We will construct some Möbius bands and verify this observation. But is it possible for a Möbius band to have two sides? We will see that the number of sides of a geometric object is not an intrinsic property of the object but instead depends on the space around it. In 1946, Martin Gardner wrote a short story about topologists who folded themselves into no-sided Möbius bands. Where can we find one of these?

Palenske 2273:30 PM

All are welcome!

Pi Day celebrates on of the most famous mathematical constants, pi.

Click on the above picture for your very own printable Pi poster.In celebration of Pi day, everyone is invited to join the department in Planeske/Putnam 229 for pie at 1:59 pm.

Bruce Berndt, '61

Professor

Mathematics

University of Illinois

Urbana, Illinois

Srinivasa Ramanujan was the greatest mathematician in the history of India. He was born in southern India in 1887 and died there in 1920 at the age of 32. He had only one year of college, but his mathematical discoveries, made mostly in isolation, have made him one of 20th and 21st centurys' most influential mathematicians. An account of Ramanujan's life will be presented. Most of Ramanujan's mathematical discoveries were recorded without proofs in notebooks, and a description and history of these notebooks will be provided. A lost notebook of Ramanujan was found in 1976. We shall also give a history and description of the lost notebook. The lecture will conclude with a brief survey of the areas of mathematics to which Ramanujan made profound contributions.

Palenske 2273:30 PM

All are welcome!

David Austin

Professor of Mathematics

Grand Valley State University

Allendale, MI

SET is a simple card game based on pattern recognition that can challenge both children and adults. It also has a surprisingly rich underlying mathematical structure that ties together ideas from a range of subjects including geometry, combinatorics, and linear algebra. In this talk, we will consider some simple questions that arise when playing SET and investigate the mathematical ideas that provide answers. We will also describe some recent and deep work from last year that gives a surprising result about a generalization of SET.

Palenske 2273:30 PM

All are welcome!

Zala Films (Video)

"From the Julia Robinson and Hilbert's Tenth Problem is a video portrait of Julia Robinson. The biographical documentary features a heroine, captivated by the lure of unsolved mathematical problems, who rises against formidable obstacles to assume a leading role in her field. Robinson's pursuit of these problems, and one in particular—Hilbert's tenth problem—brought her face to face with critical developments in 20th century mathematics. The film presents Robinson's life in the context of the 70-year search for a solution to the tenth problem.

Julia Robinson's work hinged on the ideas of key protagonists in the history of mathematics and logic: David Hilbert, Alfred Tarski, Alan Turing, and Kurt Gödel, among others. The film interweaves the personal story of this important figure in American mathematics with the discovery of new ideas that led to the development of computers."

3:30 PM

All are welcome!

Andrés Eduardo Caicedo

Associate Editor

Mathematical Reviews

Ann Arbor, MI

I present a brief overview of classical Ramsey theory, and discuss some extensions in the context of small infinite ordinals.

Palenske 2273:30 PM

All are welcome!

Oreyana Curry

Student

Albion College

Albion, Michigan

I will be giving a talk about teaching mathematics in an alternative high school vs. a public high school. In my time here at Albion I have had the opportunity to work with students in Marshall Alternative/Opportunity High School and Marshall High School. This talk will cover topics like: high school math standards, expected behaviors of high school students, alternative education vs regular education and the personal relationships a teacher builds with their students.

Palenske 2273:30 PM

All are welcome!

Drew D. Ash

Adjunct Assistant Professor

Albion College

Albion, Michigan

The purpose of this talk is to expose the audience to subfield of dynamical system called ergodic theory. To do so, we will consider the following question. How many numbers in $[0,1)$ are there when we look at their base-10 decimal expansion have the following property: The asymptotic (or expected) frequency of seeing the digit $d$, $d\in\{0,1,\dots,9\}$, is $1/10$? Can you even think of a number that has this property? We will show, using ergodic theory, that a surprising amount of numbers have this property! If time allows, we will discuss another interesting transformation called the Gauss map. The Gauss map has connections with continued fractions!

Palenske 2273:30 PM

All are welcome!

David A. Reimann

Professor

Albion College

Albion, Michigan

A degree in mathematics or computer science is excellent preparation for graduate school in areas such as mathematics, statistics, computer science, engineering, finance, and law. Come learn about graduate school and options you will have to further your education after graduation.

Palenske 2273:30

All are welcome!

Lauren Keough

Assistant Professor

Grand Valley State University

Allendale, Michigan

Graph theory is the study of relationships that come in pairs. There are many such relationships occurring naturally, think of matching medical students to residencies, friendship on social networks, or even pairing animals with the regions in which they live. From these relationships we can draw graphs. For example, for each person on a social network draw a dot, and draw a line segment between two dots if the people are "friends". Graph theory is, broadly, the study of these pictures with these dot lines. So, what could extremal graph theory be? Unfortunately extremal graph theory is not doing graph theory while snowboarding. Think of "extremal" more like you may have in Calculus 1 — perhaps you remember finding "local and absolute extrema." By the end of the talk you'll be able to ask and answer extremal questions and perhaps even know a new card trick.

Palenske 2273:30 PM

All are welcome!

Darren E. Mason

Professor

Albion College

Albion, Michigan

The Black-Scholes option pricing formula is a 1997 Nobel Prize winning result in economics
(& mathematical finance) that provides a framework for rational pricing of a large class of
stock options. In this talk we will discuss the basic idea of an option on an asset as well as
the problem of fair valuation of such a financial object. Then, assuming that the stock price
*S _{t}* follows a geometric Brownian motion, we will discuss a rough hedging argument that
results in the Black-Scholes partial differential equation as a necessary condition for risk-free
portfolio evolution. Using changes of coordinate systems and integrating factors, the Black-Scholes partial differential equation will be transformed into the classic heat (or diffusion)
equation, for which a standard integral solution form is known. Finally, we will use this
integral solution to derive the celebrated Black-Scholes option pricing formula. Some
limitations of this model will also be discussed.

3:30 PM

All are welcome!

David A. Reimann

Professor

Albion College

Albion, Michigan

Symmetric patterns are used in many situations to decorate an object with a repeating motif that is translated, rotated, or reflected without changing size. We will see examples of several symmetry types and look at these from the vantage point of group theory. In particular, we will study rosette patterns, frieze patterns, wallpaper patterns, and patterns on the sphere. We will then see how we can create all these pattern types with a unified framework based on the vectors and matrices of linear algebra.

Palenske 2273:30 PM

All are welcome!

Michael R. Elliott

Professor Biostatistics, Research Professor, Survey Methodology

University of Michigan

Ann Arbor, Michigan

I will talk about the opportunities available for graduate study in survey methodology and/or biostatistics at the University of Michigan. Undergraduate majors in mathematics, computer science, biology, economics, political science, or related fields who are considering graduate school are welcome to attend and learn about the exciting opportunities these programs offer. The Program in Survey Methodology degree combines aspects of psychology, sociology, statistics, and information and data science to provide training in topics relevant to the understanding of human populations. Students who graduate from this program can pursue careers in public health, business, public policy, consulting, and academics. Everyone is familiar with political polling, but survey methodologists also help with understanding the spread of disease, the risk of transportation injuries, the lifetime antecedents to a healthy old age, the marketing for new and existing products, among many, many care er paths. Biostatistics is an equally interesting field; biostatisticians work to unravel genetic basis of human health and disease, design and analyze data from clinical trials for new drugs, and design life-saving systems to prioritize who gets organ transplants, among many other opportunities. I have appointments in both programs and will compare and contrast the fields and the graduate programs at the University of Michigan.

Palenske 2273:30 PM

All are welcome!

Michael A. Jones

Associate Editor

Mathematical Reviews

Ann Arbor, MI

There are an infinite number of parabolas through any three non-collinear points. In this talk, I'll explain how solving a system of three equations and three unknowns and applying rotation matrices can be used to find the parabolas. The parabolas form a one parameter family. Geometric intuition about when a parabola doesn't exist for three specific values of the parameter is verified by recognizing when the equation for the parabola is undefined. Looking at the family from a calculus perspective, one can find the parabola with the widest mouth through the three points. We will use Desmos online software to visualize all the parabolas for an example. This talk is based on an article of the same title that is co-authored with Stanley R. Huddy and is forthcoming in the July 2018 issue of The Mathematical Gazette.

Palenske 2273:30 PM

All are welcome!

January | ||||||

Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |

1 | 2 | 3 | 4 | 5 | 6 | 7 |

8 | 9 | 10 | 11 | 12 | 13 | 14 |

15 | 16 MLK Day - no classes | 17 First day of classes | 18 Course Introductions Chapter 1 | 19 Math/CS Colloquium: Stephen Oloo | 20 Java Refresher Chapter 1 | 21 Week 1 |

22 | 23 Java Refresher Chapter 1 | 24 Last day to Drop and/or Add a course | 25 Java Objects Chapter 2 | 26 | 27 Java Objects HW 0 | 28 Week 2 |

29 | 30 Inheritance Chapter 2.1-2.3 | 31 Last day to register for CR/NC option |

February | ||||||

Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |

1 Exceptions, Casting, Generics Chapter 2.4-2.6 | 2 Math/CS Colloquium: Ursula Whitcher | 3 Arrays Chapter 3.1 | 4 Week 3 | |||

5 | 6 Singly Linked Lists, Equivalence, Cloning Chapter 3.2, 3.5, 3.6 | 7 | 8 Circularly Linked Lists, Doubly Linked Lists Chapter 3.3-3.4 | 9 Math/CS Colloquium: David A. Reimann | 10 Analysis of Algorithms Chapter 4.1-4.2 | 11 Week 4 |

12 | 13 Analysis of Algorithms Chapter 4.1-4.2 | 14 | 15 Chapter 4 | 16 Math/CS Colloquium: Chris Creighton, '11 | 17 Recursion Chapter 5 | 18 Week 5 |

19 | 20 Stacks Chapter 6 | 21 | 22 Queues Chapter 6 | 23 Math/CS Colloquium: Darren Mason | 24 Deques Chapter 6 | 25 Week 6 |

26 | 27 Test #1 | 28 |

March | ||||||

Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |

1 Positional Lists Chapters 7 | 2 Math/CS Colloquium: Robert Messer | 3 Iterators Chapters 7 | 4 Spring Break Week 7 | |||

5 Spring Break | 6 Spring Break | 7 Spring Break | 8 Spring Break | 9 Spring Break | 10 Spring Break | 11 Spring Break Week 8 |

12 Spring Break | 13 Trees Chapter 8 | 14 Pi Day | 15 Trees Chapter 7 HW 4 | 16 | 17 Trees Chapter 7 | 18 Week 9 |

19 | 20 Academic Advising | 21 Academic Advising | 22 Academic Advising | 23 Math/CS Colloquium: Bruce Berndt, '61 Academic Advising | 24 Academic Advising | 25 Week 10 |

26 | 27 Academic Advising | 28 Academic Advising | 29 | 30 Math/CS Colloquium: David Austin | 31 |

April | ||||||

Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |

1 Week 11 | ||||||

2 | 3 | 4 | 5 | 6 Math/CS Colloquium: Zala Films (Video) | 7 | 8 Week 12 |

9 | 10 | 11 | 12 | 13 Math/CS Colloquium: Andrés Eduardo Caicedo | 14 Good Friday No Afternoon Classes | 15 Week 13 |

16 | 17 | 18 | 19 | 20 Honors Day | 21 | 22 Week 14 |

23 | 24 | 25 | 26 | 27 Math/CS Colloquium: Oreyana Curry Last day of classes | 28 Reading Day - no classes | 29 Final Exams Week 15 |

30 Final Exams |

May | ||||||

Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |

1 Final Exams | 2 Final Exams | 3 Final Exams | 4 | 5 | 6 Week 16 | |

7 | 8 | 9 | 10 | 11 | 12 | 13 |

14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 |

28 | 29 | 30 | 31 |

Copyright © 2017, David A. Reimann. All rights reserved.