NS

Undergraduate // Majors // Natural Sciences Concentrations

Problem Solving in Complex Systems

Analyze complex systems at the levels of atoms, molecules, and the Earth in order to understand and design solutions to the 21st century environmental and health challenges facing our world.

Core courses

Problem Solving in Complex Systems (Natural Sciences Major)

In their second year, Natural Sciences majors enroll in core courses that provide the foundation for the Natural Sciences concentrations. They also take electives from core courses offered in other majors.


NS110L / Physics of Life

We explore how physics, ranging from mechanics through atomic physics, can be applied to the life sciences. Examples of applications are: fluid flow and heat regulation in biological organisms, electrostatics in the nervous system, and wave phenomena in hearing and vision. The course emphasizes the development of tools and problem-solving approaches needed to describe the physical phenomena at hand.

Prerequisite: CS51 / Formal Analyses

Corequisite:

NS110U / Physics of the Universe

We use gravitational and electromagnetic interactions as representatives for how physics takes experimental evidence and then encodes it into a theoretical framework that can be used to make predictions and draw inferences about new phenomena. The course emphasizes the development of the tools needed to describe the physical structure of nature and then uses these tools to infer the domain of validity of theories in physics and what might lie beyond them.

Prerequisite: CS51 / Formal AnalysesCS111 / Single and Multivariable Calculus

Corequisite:

NS111 / Implications of Earth's Cycles

The Earth system is investigated from its origin to its functioning today. Beginning with the origin of the Universe and the creation of elements in stars, the course progresses to an understanding of solar systems and the conditions that gave rise to habitable planets. Earth evolved from a lifeless, reduced planet with a simple mineralogy to a complex, oxidized planet that can support advanced life such as human beings. An aim of the course is to place human beings in a universal and planetary context, and to see the steps in planetary evolution as an essential perspective on how we relate to Earth today. This course qualifies as part of the Interdisciplinary Minor in Sustainability because it addresses the evolution of Earth and the natural processes regulating the planet. In order to sustainably care for the planet, it is essential to understand the systems and processes operating on Earth from climate regulation to natural resource formation and how human activities impact these processes.

Prerequisite: NS51 / Empirical Analyses

Corequisite:

NS112 / Evolution Across Multiple Scales

“Nothing in biology makes sense, except in the light of evolution” – T. Dobzhansky. From the relationships among species in a forest to the interactions of molecules in a cell, evolution is ultimately responsible. One might be tempted to view Dobzhansky’s quote as indicating that evolution is one key that unlocks the complexity of biology. That view is supported by statements such as “survival of the fittest,” which oversimplify the complexity of evolution. Instead, Evolution at Multiple Scales views evolution as the elaborate set of interconnected concepts it is. Although Darwin published On the Origin of Species over 150 years ago, evolutionary biology continues to be augmented, as new discoveries are driven by new technologies. By evaluating evolutionary concepts in a broad range of biological scenarios, students deepen their understanding of evolution itself, shedding light on the diversity of life it has produced. This course qualifies as part of the Interdisciplinary Minor in Sustainability because it addresses biodiversity. NS112 focuses on the evolutionary processes producing biodiversity, and also addresses the benefits of biodiversity to humans, the consequences of biodiversity loss, and strategies to maintain it.

Prerequisite: NS51 / Empirical Analyses

Corequisite:

NS113 / Chemical Structure and Reactivity

This course explores the physical and chemical properties of nature based on molecular, atomic, and sub-atomic structures, with an emphasis on how structure determines reactivity. Empirical observations will be combined with the principles of chemistry and physics to understand the microscopic properties of nature that underpin phenomena at various scales. Students who complete this course will be able to generate strong mechanistic chemical explanations and apply them in advanced chemistry, physics, earth science, and biology courses.

Prerequisite: NS51 / Empirical Analyses

Corequisite:

Concentrations Courses

Problem Solving in Complex Systems (Natural Sciences Major)

In their third year, Natural Sciences majors select a concentration, begin taking courses within it and begin work on their capstone courses. They also take electives chosen from other Minerva courses (other concentration courses in Natural Sciences, core and concentration courses in other colleges). Natural Sciences offers concentrations shown in the table below.

In the fourth year, Natural Sciences majors enroll in additional electives chosen from Minerva’s course offerings within or outside the major. Additionally, they take senior tutorials in the major, and finish their capstone courses.

NS162 / Statistical Mechanics: Theory and Applications

Statistical Mechanics describes how macroscopic systems and the macroscopic physical laws that govern them emerge from the aggregated behavior of many microscopic components. The field developed to explain the empirical results of thermodynamics in terms of the microscopic theory of atoms — Why do macroscopic systems have uniform properties? How do equations of state emerge from microscopic dynamics? When do these emergent laws break down? Why does the 2nd law of thermodynamics emerge, and how does it relate to phenomena from the efficiency of engines to the cooling of the universe? Why does matter have phases and under what conditions do phase transitions occur? While we primarily focus on explaining the tools of statistical mechanics through thermodynamics, we also discuss applications of these tools to computer science, machine learning, finance, and modeling social systems. In doing so, we introduce the basics of information theory and develop the connections between thermodynamic entropy and the more broadly applicable concept of Shannon entropy. NOTE: In addition to the listed prerequisites, the following courses are recommended prior to taking this course: CS114

Prerequisite: CS111 / Single and Multivariable CalculusNS110L / Physics of LifeNS110U / Physics of the UniverseNS113 / Chemical Structure and Reactivity

Co-rerequisite:

NS164 / Solutions From and For Life

Explore cutting-edge solutions to difficult problems in human health. Learn the process by which drugs are discovered and designed, how stem cells are engineered to form tissues, and how genes can be engineered for a multitude of purposes. Analyze how to determine what solutions can be applied to what problems and how to communicate advances in biotechnology to expert and public audiences. NOTE: In addition to the listed prerequisites, the following courses are recommended prior to taking this course: NS113, NS144, NS154, CS130

Prerequisite: NS112 / Evolution Across Multiple Scales

Co-rerequisite:

NS166 / Keeping Earth Habitable

Examine environmental and natural resource issues such as pollution, deforestation, climate change impacts, habitat loss, agricultural impacts, and the potential impact of human population growth and consumption. Consider systems challenges and potential solutions including social, political, economic, and technological approaches to major environmental problems. Note: This course is required for the Interdisciplinary Minor in Sustainability. Students not majoring in NS but with a declared minor in Sustainability may enroll in NS166 without completing the prerequisites (NS111 and/or NS112). This course takes an in-depth look at environmental and natural resource issues such as pollution, habitat loss, and climate change impacts and then explores potential solutions. Effective solutions to “keeping Earth habitable” require combining social, political, economic, technological, and ethical approaches.

Prerequisite: NS111 / Implications of Earth's CyclesNS112 / Evolution Across Multiple Scales

Co-rerequisite: