This course traces knowledge of the universe from astronomy’s ancient roots to the modern study of extrasolar planetary systems, cosmology, and black holes. Topics include Newton’s laws of motion and universal gravitation, Kepler’s laws, orbital dynamics, and space travel. Additionally, students will contemplate the nature of light, the nature of matter, and nuclear physics. This knowledge to will be used to explore the properties of our sun, solar system, further galaxies, the creation of chemical elements, and the expansion of the universe. By the end of the course, students will be prepared to explore dark energy and the fate of the universe as we know it.

Environmental challenges are perhaps the greatest challenges that society faces today. Building societies that manage our natural resources in ways that do not diminish the ability to provide for future generations includes exciting new approaches from many disciplines including science, engineering, economics, sociology and political science. 

In this course, students will use a systems-approach to problem formulation and solving as they investigate ecosystems, food systems, energy systems, and architecture. Students will learn using material from interactive lectures, laboratory work, engineering design projects and field experiences.  Lectures on ecological restoration, regenerative agriculture, energy efficient building and transportation design will provide background for field trips to the Hudson River, Billion Oyster Project, Vertical Farms, and examples of Green architecture. Hands-on activities will include water quality testing, air quality testing, building solar cars and water wheels. Students will then select, develop and evaluate case studies on different aspects of building a sustainable future!

Is the universe infinite or finite? What is the curvature and overall shape of the space we live in, and how might we detect this? In this course, participants learn how models for topological spaces relate to theories on the shape of the physical universe. Philosophical discussions are informed by pencil and paper computations, experiments with common household materials, and interactive online games and modules.Participants gain, in addition to early exposure to modern content at the intersection of topology and physical cosmology, an appreciation for rigorous mathematical thinking that is motivated not so much by numbers and quantity as by profound questions about the nature of our world.

Chemistry, the central science, is the science of molecules and bonds. Its signature is change in all its manifestations, from events that happen on a geological time scale to those that happen instantaneously, from the cosmological to the subatomic scale. Chemistry provides powerful scientific tools that extend our ability to sense the magnitudes of change by stretching the limits of what we know of our universe.

Intensive Seminars in Modern Chemistry is designed for highly motivated students who want to strengthen their understanding of chemistry and current research methods. The daily program follows a seminar format, beginning with a presentation by senior faculty members and researchers that is expanded upon through small group discussions and laboratory experiences. 

Topics have been selected because they stand out as essential themes of current research, illustrate the methods of science, lend themselves to historical development, and highlight the role of chemistry as the central science. Through integrative experiments and collaborative projects, students discover the synthetic and analytic dimensions of chemistry in forensic, environmental, and materials problems. Experiments emphasize the development of problem-solving and critical thinking skills.

Formal training includes instrumental methods in spectroscopy, chromatography, magnetic resonance, and computer simulations with state-of-the-art equipment in the department’s modern laboratories. Guest lecturers and field trips to area research facilities round out the program. Students are expected to complete a small research project, prepare a scientific paper, and participate regularly in class discussions.
 

The progress of civilization is inscribed in the history of humans and their materials—the Stone Age, the Iron Age, and today’s Age of Plastics. Materials determine the technologies that provide protection, communication, information, construction, mechanization, agriculture, and health. Knowing why glass shatters, wood splinters, steel is tough, rubber stretches (and recovers), nylon can be drawn, and tin flattens makes possible the selection of materials for enormously different applications. Engineers are mostly successful at designing and manufacturing objects and devices, but on occasion there are catastrophic failures—bridges collapse, airplanes fall from the sky, containers leak, pipes burst, and the electrical grid goes down, leaving us cold and in the dark. And there are the annoying little failures—light bulbs burn out, clothes become permanently stained, foods spoil, and batteries die.

In this challenging course, participants experience a hands-on introduction to materials science, engineering, and technology, from the bulk properties of the solid state to the nanoscale properties of large and small molecules and single atoms. Special attention is given to nanoscale materials and devices because of their potential for defining the next generation of important materials and machines. It has been said that the nanoscale is the new frontier of science and technology.

Students investigate these worlds in a discovery-based environment, working under the guidance of an experienced instructor and a team of assistants, research scientists, and technologists from Columbia’s Department of Chemistry and from industry and national laboratories. The studio classroom format integrates laboratory and lecture and encourages teaching and learning especially useful to those considering undergraduate studies in engineering and science.

This curricular option familiarizes students with the foundations of physics and chemistry from a modern perspective.

Lectures, discussions, and simulations focus on topics such as electromagnetic radiation, spectroscopy, elementary particles, the quantum mechanics of atoms, special relativity, and gravitation.

Simulations and virtual experiments concentrate primarily on the interference of electromagnetic waves, the orbital motion of planets, and conservation laws.

Designed for aspiring physicists and mathematicians, students will delve into the powerful mathematical tools essential for understanding and solving complex physical problems.

Students will develop an understanding of these methods by learning to model, analyze, conduct theoretical investigations and interpret physical phenomena. Through engaging lectures, hands-on problem-solving, and interactive projects, participants will gain proficiency in applying concepts to real-world scenarios. Emphasis will be placed on developing critical thinking skills and intuition to tackle challenges encountered in theoretical and experimental physics.

This course provides a valuable head start for those planning to pursue studies in physics, engineering, mathematics, or related fields at the collegiate level. 

This course delves into the fundamentals of Quantum Computing, bridging the gap between quantum mechanics and its groundbreaking applications in computing. It focuses on developing students’ knowledge and skills in modern quantum technologies with numerous real-world applications. The course will include lectures emphasizing conceptual understanding and problem-solving, as well as essays and group projects to foster collaborative learning.

Topics include:

• Quantum Mechanics Foundations: Understanding quantum states, superposition, entanglement, and the evolution of quantum systems.
• Quantum Bits (Qubits): Exploration of qubits as the basic units of quantum information and their state manipulation.
• Quantum Algorithms: Introduction to key algorithms like Shor's algorithm for factoring and Grover's search algorithm.
• Quantum Computing Models: Study of quantum circuits, quantum gates, and error correction.
• Quantum Technologies: Insight into current quantum computing hardware and future prospects.

This course is designed for motivated high school students who want to expand their knowledge of modern physics and be at the forefront of technological innovation.

What makes the universe tick? At the heart of modern physics lies Einstein’s theory of special relativity—a revolutionary idea that redefined time, space, and energy. From the iconic equation E=mc2 to the strange realities of time dilation and length contraction, this course invites you to explore the concepts that forever changed how we understand the cosmos. Along the way, you’ll see how Einstein’s ideas influence everything from black holes to interstellar travel, laying the groundwork for some of today’s most thrilling scientific discoveries.

In this three-week journey, you will delve into the foundational principles of special relativity, including spacetime, Lorentz transformations, and the interplay between relativity and electromagnetism. You’ll also connect these ideas to larger concepts like the Doppler effect and general relativity, gaining a preview of college-level physics without getting bogged down in heavy mathematics. With thought experiments, interactive discussions, and real-world applications, this course is perfect for students eager to uncover the elegance and mystery of Einstein’s legacy. 

The origin and evolution of the Universe is one of the greatest (and oldest) questions ever asked. In a little over a century, cosmology has matured as a discipline due to improvements in our understanding of fundamental physics and technological advances allowing us to map the Universe in unprecedented detail and perform complex calculations. This course is an introductory review of the field of cosmology for students with a background in physics and math, but not necessarily astronomy.  The course focuses on the field of cosmology, its early history, and its relationships to observational astronomy and particle physics.  We will discuss the observations that led scientists to believe that the Universe is expanding, explanations for the expansion, the origin of the Universe and the evolution of its constituent materials, including dark matter and dark energy.  We will also discuss general relativity and its implications for the structure of the Universe, its history, and predictions regarding astrophysical phenomena such as black holes.  In-class discussions and activities based on primary source research papers will complement in-class problem solving and supplemental readings.

Quantum mechanics is the science of the “small”; understanding how matter and light behave. An exciting application of modern physics, the field focuses on computing objects such as expectation values, vector evolution, and decoherence times through linear algebraic frameworks. The result of this work includes advancements in cybersecurity, electronics, aviation, communications, and engineering (to name a few). 

Through this course, students will explore the basics of theoretical foundations, equations, computations, and principles that impact the way we live today, and our future. Beginning with an exploration of topical ideas from  popular physicists, students will work through probability theory that will lead to sophisticated explanations of the world, as well as computations that will provide an elevated level of awareness for how humans work and play. By the end of the course, students will look at the world differently, and be prepared for more sophisticated study in this area.