Cluster 6: Chemistry and Mathematics: From Life to Thought
Chemistry and mathematics are combined in this cluster for a fun and challenging mix of different kinds of activities and ideas. In the chemistry course, students will explore how basic chemical processes enhance many aspects of life, from medicines to blue jeans to fireworks, as well as investigate key concepts including the origin of life on earth. In the math course, students will discuss and explore the logical foundation of mathematics and how it pertains to solving problems. Students will do this in theory and practice by studying basic logic as well as wracking their brains with a myriad of ancient and modern problems. Come prepared to think about these topics in new ways, learn, and have fun.
Prerequisite: Students must have completed one year of high
school algebra and chemistry and demonstrated maturity in laboratory
safety.
All students in this cluster will be enrolled in the following
courses.
Enhancing the Quality of Life: Colors, Fragrances, and Pharmaceuticals
Instructors: Professors Bakthan Singaram (Chemistry and Biochemistry Department) and Stanley Williamson (Chemistry and Biochemistry Department)
This will be unlike any chemistry course you've ever had! Instead of using a textbook, we will use the literature and the laboratory to address the impact of chemistry on society. We will discuss basic chemical principles to discover how chemistry affects every aspect of our lives, including medicine, computers, food flavors, dyes, polluting compounds, and even how life began on the earth. We will perform experiments, not just watch demonstrations. At the end of four weeks you will have the opportunity to participate in a poster seminar not unlike those presented at scientific symposia around the world. You will take an intellectual as well as physical giant step toward your future as a scientist and innovator.
Logic, Riddles, Paradoxes
Instructor: Frank Bäuerle, Ph.D. (Mathematics Department)
The basic goal in this course is for students to wrack their brains, have fun while they are doing it, and at the same time gain insight into the inner-workings of mathematics. The students' work is loosely grouped into the following four categories.
To infinity and beyond: Students will be exposed to some of the most surprising, interesting, and intriguing aspects of the age-old riddle of infinity. Examples are: There is always room at Hotel Infinity; Countability of the integers and rationals; Can you list the real numbers?; Cantor's Diagonalization Method; The Continuum Hypothesis.
Paradoxes: Students will be confronted with statements that are strange, weird, and sometimes even false. Examples are: Russel's "Salon Paradox" (a paradox on self-referentiality). Epimenides' "Liar's Paradox" (a paradox on self-referentiality). Zeno's "Achilles vs. the Tortoise Paradox" (a paradox on infinity, or how infinitely much stuff doesn't account for much).
Logical Systems: Students will study and practice the basic workings of logical systems. Examples are: Truth tables of logical connectors (and, or, implies, etc.); Tautologie; Natural deduction system for proofs; Sufficient and necessary conditions on sorting your socks into pairs.
Riddles and brain teasers: Students will wrack their brains solving these puzzles from ancient to modern times. A typical example is the following Pirate Problem: A pirate ship captures a treasure of 1000 golden coins. The treasure has to be split among the 5 pirates:
1, 2, 3, 4, and 5 in order of rank. The pirates have the following important characteristics: infinitely smart, bloodthirsty, greedy. Starting with pirate 5 they can make a proposal how to split up the treasure. This proposal can either be accepted or the pirate is thrown overboard. A proposal is accepted if a majority of the pirates agree on it (a tie means the proposal is rejected). What proposal should pirate 5 make? What happens if there are 6, 7 or more pirates? Generalize!
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
