Fall 2022

ASTRONOMY AND ASTROPHYSICS: This course will trace our knowledge of the Universe from astronomy's ancient roots in naked eye observations of the sky to the twenty first century studies of extrasolar planetary systems, black holes, and cosmology. Initial topics will include: Newton's laws of motion and gravitation, orbits and space travel, and the properties of planets' surfaces, interiors, and atmospheres. The course will then combine atomic and nuclear physics with stellar and galactic astronomy to describe stars, supernovae, black holes, the interstellar medium, galaxies, the creation of the elements, and the evolution of the universe.

RELATIVITY: The course will present Einstein's special relativity, including topics such as Galilean relativity, Einstein's postulates, time dilation, length contraction, failure of simultaneity at a distance, Lorentz transformations, space-time, four-vectors, the relativistic Doppler effect, Compton scattering, the Einstein and de Broglie relations, and mass-energy equivalence. A brief interlude to general relativity covers the equivalence principle and gravitational redshift.

ORGANIC CHEMISTRY: This course combines lectures, virtual laboratory experiments and demonstrations to provide an introduction to the principles and exciting frontiers of organic chemistry. Students will be introduced to the synthesis of organic compounds and the reaction mechanisms. Lecture topics will include: chemical bonds, structural theory and reactivity, design and synthesis of organic molecules, and spectroscopic techniques (UV-Vis, IR, NMR) for structure determination. Recordings of experiments and follow-up discussions will introduce common techniques employed in organic chemistry and will include: extraction, recrystallization, thin layer and column chromatography, reflux, and distillation.

CLASSICAL AND QUANTUM COMPUTING DEVICES: This course will introduce students to various techniques used to create micro-/nano-structures, with an emphasis on devices for classical and quantum information processing. Starting with the pioneering ideas presented by Richard Feynman in his paper 'Plenty of Room at the Bottom', students will learn how those visionary proposals have developed into a discipline undergoing an exponential growth and extremely rapid innovation, particularly CMOS (complementary metal-oxide semiconductor) technology. The course will include virtual experiences including a visit to see fabrication facilities and metrology/microscopy tools in quantum materials labs on the Columbia campus. Students will have the opportunity to write basic programs to run on IBM's quantum circuit interface. The course will conclude with introductory lectures on quantum mechanics and the physics of solids as it relates to quantum information science and technology while maintaining the focus on the experimental and practical aspects of the discipline.

INTRODUCTION TO ALGORITHMS: This course motivates algorithmic thinking. The key learning objectives are the notions of run-time analysis of algorithms, computational complexity, algorithmic paradigms and data structures. Content will primarily be based on high-school algebra and calculus. A tentative list of topics includes: run-time analysis of algorithms, basic sorting algorithms, quick sort, binary sort, heap sort and hash table. If time permits, graph algorithms and dynamic programming will be covered.

COMPUTER PROGRAMMING IN JAVA: Students will learn the basics of programming using Java. Topics will include: variables, operators, loops, conditionals, input/output, objects, classes, methods, basic graphics, and fundamental principles of computer science. Approximately half of the class time will be spent working on the computer to experiment with the topics covered. Some previous programming experience will be helpful but is not required.

GRAPH THEORY BY EXAMPLE: Graph theory is a new and exciting area of discrete mathematics. Simply put, a graph is just a collection of points joined by certain pairs of these points, yet many real-world problems (i.e. traffic flow, school admissions, scheduling) can be formulated as such. Although many problems in graph theory can be easily stated, these problems often have complex solutions with far reaching implications and applications. Problem solving, class discussions, and student examples will be the major proportion of this course. Rigorous proofs will also be presented in the lecture. In addition to exploring the mathematics of graph theory, we will also see how graph theory arises in fields such as computer science, chemistry, game theory, and many others.

Columbia University Science Honors Program.