Cluster 7: Astronomy, Number Theory and Cryptography: From 1 to the Stars
The National Science Foundation-sponsored Center for Adaptive Optics (CfAO) along with COSMOS, host a cluster which includes two coordinated courses on astronomy and mathematics. In the astronomy course students will learn about how astronomers examine the universe with a focus on the physics of light and advanced technologies such as adaptive optics, a new technique that makes images from ground-based telescopes as sharp as images taken from space. In the number theory course and cryptography course, students will study number theory, and how basic properties of the integers are used to create `unbreakable' codes, like the ones banks use to keep on-line banking safe. In both courses, students will see how pure theory is translated into practical and important applications.
Prerequisite: Completion of one year of high school level mathematics.
Preference: Completion of two years of high school level mathematics.
All students in this cluster will be enrolled in the following
courses.
Astronomy Today: Observing the Universe
Instructor: Puragra Guha thakurta (UCO/Lick Observatory, Astronomy/Astrophysics)
The course will begin by taking students on a tour of objects in the universe and their relative sizes and scales. Then students will learn about the physics of light and optics and how telescopes work. In the final lectures, we will be exploring new and advanced technologies such as very large telescopes and space telescopes, as well as adaptive optics, a new technique that makes images from ground-based telescopes as sharp as images taken from space.
The most exciting part of this course will occur in the final two weeks of the program when students will get to apply what they have learned to an astronomical research project. Students will be involved with every aspect of the project, from the acquisition of data at the telescope to the final analysis of the results.
The first weeks of the course will be a combination of lectures and labs, while during the last weeks students will be primarily working in groups on research projects. We are also planning a field trip to Lick Observatory on Mount Hamilton so that students will get to see a working research observatory.
Number Theory and Cryptography
Instructor: Yonatan Katznelson, Ph.D. (Economics Department)
Both the theory of numbers and cryptography have been around for thousands of years, and there have always been connections between them. In the past 30 years the interaction between number theory and cryptography has grown tremendously, fueled by the need to transmit information safely on computer networks, like the internet. In this course, we'll explore the integers and their properties and see how number theory is used in the construction of crypto-systems. One of the topics we'll study in some detail is the distribution of prime numbers among all the integers, and why prime numbers are so important to cryptography. Until we meet this summer, here is a simple encrypted message for you to work on: EHZDUHWKHLGHVRIPDUFK.
Hint: The code is famous, and the message is appropriate.
Transferable Skills: Tools for Success
It may or may not surprise you that being a university researcher
requires a whole host of skills outside of the specific scientific
knowledge required of your chosen discipline or specialty. It requires
communication skills such as the ability to present your work in
writing and orally. It requires competencies in the realm of information
technology including the ability to find and judge (the validity
of) information and use a variety of hardware and software tools
(e.g. spreadsheets, databases, statistics software, other data manipulation
tools). It requires all of those skills required to effectively
conduct research such as data collection, analysis and interpretation,
critical thinking and problem solving as well as the ability to
conduct laboratory and/or field work. And, of course, a baseline
competency in English, science, mathematics and computers is critical.
The governing mission of the UCSC COSMOS Transferable Skills course
is to promote students’ future academic (and professional)
success through the exploration and development of transferable
skills: i.e. those competencies that students develop while in school
which facilitate academic achievement, the eventual transition into
the work-force and which are applicable in many other life situations.
Go to course information for:
- Logic and Probability: Reason and Riddles*
- Engineering
the Future: Autonomous Robots and Nanotechnology*
- Under
the Sea: Exploring Marine Organisms and Their World*
- Everyday
Chemistry: From Perfumes to Pollution*
- Video Games: The Design of Fun - From Concept to Code*
- Chemistry
and Mathematics: From Life to Thought*
- Astronomy, Number Theory, and Cryptography: From 1 to the Stars*
- Marine Mammals and Oceanography: From Prey to Predators
- Particle and Astrophysics: Investigations of the Minuscule to the Massive
