Cluster 7: Points in Space: Astronomy and Linear Algebra
In this cluster, you will study things ranging from the very concrete structure of stars and galaxies to the very abstract structure of vector spaces.
Astronomy is concerned with the study of the physical space of the universe, the objects that fill it, its various structures and the physical laws that govern it. 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.
Linear Algebra is also concerned with the study of space. More precisely, Linear Algebra studies vector spaces, their structures and sub-structures, and the mathematical laws that govern these spaces and the maps between them. In the Linear Algebra course, you will study how problems from the real world motivate the abstract world of mathematics, and how mathematics is used to solve real-world problems.
MATLAB student software was graciously provided by MathWorks.
Prerequisite: 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.
Linear Algebra
Instructor: Yonatan Katznelson, Ph.D. (Applied Mathematics Department)
Linear algebra is one of the most useful, and therefore important, fields in mathematics. It begins with the study of systems of linear equations and the nature of the solutions of these systems, but it goes well beyond that. MATLAB is a software package for doing mathematics on computers, and it is particularly useful for solving problems in linear algebra.
In this course we'll study the theory behind systems of linear equations and their solutions, including some matrix algebra, we'll learn how to use MATLAB to help us with the lengthy (and occasionally tedious) computations and most importantly, we'll study a variety of applications of linear algebra to problems from a variety of other fields, like statistics, economics and population dynamics, to name a few.
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, Cryptography and Number Theory: 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*
- Points in Space: Astronomy and Linear Algebra*
- Marine Mammals and Oceanography: From Prey to Predators
- Particle and Astrophysics: Investigations of the Minuscule to the Massive
