SCIENCE HONORS PROGRAM
COURSE DESCRIPTIONS
Spring 2023



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 AND QUANTUM PHYSICS: Relativity and quantum physics underpin much of our modern understanding of the universe. The first part of 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. The second part begins with a historical introduction to quantum physics, before moving on to topics such as wave interference, the double-slit experiment, complementarity, the Heisenberg uncertainty principle, the Bohr-Einstein debates, Bohr's atomic model, particle in a box, and zero-point energy. Advanced topics include the two-state quantum system, quantum tunneling, and the Schrodinger equation. Students should have completed pre-calculus.

SCIENCE OF MATERIALS: Almost every major technological advancement has depended on a leap in our understanding of Materials Science- we even name eras after their most important materials, from the stone and bronze ages to our modern age of steel and silicon. We will cover the main classes of materials (metals, ceramics, polymers/plastics, and functional-electronic) by understanding their structure at different length scales, from atomic bonds, to crystals, to steel in skyscrapers and silicon in transistors. We will see how the structure and defects in materials determine their properties, and how physics and chemistry can be used to engineer the materials to build the modern world, answering questions ranging from "Why are rubies red?" to "How does tempered glass protect my phone?" Topics to be covered include: atoms and bonding; crystals and defects; mechanical, electronic, and optical properties; band theory and electronic devices; graphene and 2D materials.

CLASSICAL AND QUANTUM COMPUTING DEVICES: This course will begin with the principles of quantum mechanics, showing how entanglement and superposition could usher in a new era of quantum information devices. Students will be exposed to the math underlying quantum physics, learn about the many platforms being used to build qubits in research and industry, and have the opportunity to visit a quantum optics lab at Columbia. The second part of the course will introduce students to the theory and applications of modern CMOS (complementary metal-oxide semiconductor) technology with an emphasis on devices for classical and quantum information processing. Students will examine the fabrication and implementation of conventional 3D semiconductor devices as well as the "new-age" 2D Van der Waal (VdW) materials for multi-layered heterostructure analysis. The course will also include visits to see fabrication facilities and metrology/microscopy tools in quantum materials labs on the Columbia campus.

ORGANIC CHEMISTRY: This course combines lectures, collaborative discussions surrounding laboratory experiments and theory, and online 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. Research work conducted by graduate students will introduce common techniques employed in organic chemistry and will include: extraction, recrystallization, thin layer and column chromatography, reflux, and distillation.

BIOTECHNOLOGY AND BIOENGINEERING: Biotechnology and bioengineering have transformed the world around us for countless fields, from medicine to agriculture. In this course, students will learn the fundamentals of biology and biochemistry and how scientists have taken these biological systems and engineered them to produce life-saving insulin, drought-resistant crops, COVID-19 tests, and many more topics. In each class we will learn about at least one biotechnology breakthrough, how it works, and have discussions on the greater impacts of these breakthroughs.

CODE OF LIFE: EXPLORING COMPUTATIONAL BIOLOGY*: Over the past few decades, computer science has revolutionized our approach to studying biology. In this course, we will embark on an exciting journey into the world of bioinformatics. Through interactive lectures, hands-on activities and case studies, students will gain a deeper appreciation of how computational tools are used to decode the complex biological processes that govern life on earth. The course will begin with an introduction to DNA sequencing and its applications in various fields, followed by a discussion of single-cell RNA sequencing and its role in understanding cellular diversity. We will then delve into cancer genomics and learn how to identify genetic mutations and develop targeted therapies. Next, we will explore novel machine learning approaches for predicting protein structure and function. We will also discuss computational immunology and population genetics, and their applications in personalized medicine. By the end of the course, students will have a solid foundation in the principles and applications of computational biology, and will be equipped with the skills to pursue further studies in this rapidly evolving field. Prior coding experience is useful but not required. *Students will need to be able to bring a personal laptop for this course.

HUMAN PHYSIOLOGY: This course provides an introduction to the major systems of the human body, including the cardiovascular, respiratory, digestive, endocrine, immune, and nervous systems. Discussions will progress from general system structure to function on a cellular level. An overview of pathology and current research will also be presented.

TISSUE ENGINEERING: AN INTRODUCTION TO THE WORLD OF REGENERATIVE MEDICINE: This course is designed to provide a comprehensive overview of the field of tissue engineering, from the basics of cell biology to the forefront of cutting-edge clinical developments. At the start of the course, students will learn about the composition of the extracellular matrix and its impact on how cells interact with their environment. We will then move on to discuss the potential of tissue engineering to address major medical issues and bridge the gap in transplantation by growing tissues ex vivo. Later, students will explore the various tissue engineering solutions that have been approved for clinical use, as well as the organ-on-a-chip systems and their implication for pharmaceutical development. At the conclusion of the course, students will hold a strong grasp of core tissue engineering principles, preparing them for research experiences and advanced study.

EXPLORING THE COMPLEX: AN INTRODUCTION TO COMPLEX ANALYSIS: This course will provide an introduction to the fascinating field of complex analysis. Complex analysis is a branch of mathematics that studies complex functions, which are functions that map complex numbers to other complex numbers. In this course, we will explore the properties and behavior of these functions, which can help us understand and solve problems in many different fields. After examining the basic properties of complex numbers, including complex arithmetic, complex conjugation, and the geometry of the complex plane, we will move on to more advanced topics, such as complex differentiation and integration, the Cauchy-Riemann equations, and the Cauchy integral theorem. One of the key concepts we will study in this course is analyticity, which is the property that allows us to differentiate complex functions. We will explore the relationship between analytic functions and the geometry of the complex plane, and see how analytic functions can be used to solve problems in physics, engineering, and other fields. Other topics that we may cover include complex power series, Laplace and Fourier transforms, and singularities. We will also examine the application of complex analysis to a variety of different problems, including fluid dynamics, electrical engineering, and number theory. No special mathematical background is required for this course.

SPACES AND SYMMETRIES: A large part of modern mathematics deals with understanding spaces and their symmetries. This course will serve as an introduction to the mathematical formulation of these ideas, starting with spaces (geometry and topology): when are two spaces "the same" and how can we tell when they are "intrinsically" different? In order to answer this question, we will often look at the structures arising from symmetry (group theory, algebraic topology). On the way, we will explore the mathematics of knots, singularities, alternative number systems, non-Euclidean geometries, and much more!

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. *Students will need to be able to bring a personal laptop for this course.

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. Students will need to be able to bring a personal laptop for this course. *Students will need to be able to bring a personal laptop for this course.

EXPLORATIONS IN DATA SCIENCE*: In this course, students will carry out a series of explorations in data science to learn about statistical thinking, principles and data analysis skills used in data science. These explorations will cover topics including: descriptive statistics, sampling and estimation, association, regression analysis, etc. Classes will be organized to have a lecture component and a hands-on exploration component each session. In the lecture session, an introductory curriculum on data science will be given. In the exploration session, students will be led through data analysis exercises using the statistical analysis language R. These exercises are designed to use open data, such as NYC open data that contain interesting information about neighborhoods of New York City. No prior programming experience is required. *Students will need to be able to bring a personal laptop for this course.

Columbia University Science Honors Program.