The following introductory-level courses without prerequisites enable students to fulfill the skills requirement in quantitative reasoning (Qr) through study in a wide range of quantitative disciplines. In addition, there are a multitude of Qr courses with prerequisites (such as single-variable calculus, introductory computer programming, or introductory work in a natural or social science) that can be fulfilled through introductory-level course work or advanced placement. Students may view the complete list of Qr courses or search for Qr courses in specific departments using the Yale Course Search.
Each student will wish to select courses that match his or her interests and level of preparation. Information about expected preparation is available through links following each course’s brief description.
Please note, not all courses are offered every semester:
First-year STEM Seminars 2025-26
*Limited enrollment. Pre-registration is required for all First-Year Seminars. Information regarding application procedures may be found on the program website.
- APHY 0800/EVST 0800/PHYS 0800/ENAS 0800 - Energy, Environment and Public Policy - Instructor Permission Required
Other Courses Without Prerequisites
- APHY 1000/EPS 1050/EVST 1000/ PHYS 1000 - Energy, Environment, and Public Policy Instructor Permission Required.
- APHY 4490 - Solid State Physics
- ASTR 1100 - Planets and Stars
- ASTR 1200 - Galaxies and the Universe
- ASTR 1700 - Introduction to Cosmology
- ASTR 1800 - Introduction to Relativity and Black Holes
- ASTR 2100 - Stars and Their Evolution
- ASTR 2550 - Research Methods in Astrophysics - Instructor Permission Required
- CHEM 1610 - General Chemistry I
- CHEM 1700 - Quantitative Foundations of General Chemistry
- CPSC 1001 - Introduction to Programming
- CPSC 1100 – Python Programming for Humanities and Social Sciences
- CPSC 1001 - Introduction to Programming
- CPSC 1230/S&DS 1230/PLSC 3508 – Ydata: An Introduction to Data Science
- CPSC 2020 – Mathematical Tools for Computer Science
- CPSC 3380 – Digital Systems
- ECE 3101 - Signals and Systems Prior knowledge of advanced calculus of one variable and some elementary real analysis will be very useful (something like MATH 115), although it is not required strictly.)
- ECE 3481 - Digital Systems Recommended preparation: EENG 201.
- ECE 4451 - Network Algorithms and Stochastic Optimization
- ECON 1108 - Qualitative Foundations of Microeconomics - Instructor Permission Required
- ECON 1110 - An Introduction to Microeconomic Analysis - Instructor Permission Required - Enrollment limited to first-years and sophomores. May not be taken after ECON 1108 or 1115.
- ECON 1115 - Introductory Economics: Microeconomics - May not be taken after ECON 1108 or 1110.
- ECON 2159/GLBL 2159 - Game Theory
- EP&E 4295 - Game Theory and Political Science
- EP&E 4328/S&DS 1720/PLSC 2509 - Ydata: Data Science for Political Campaigns
- ENAS 1200/ENVE 1200/CENG 1200 - Introduction to Environmental Engineering
- EPS 1050/APHY 1000/EVST 1000/PHYS 1000 - Energy, Environment and Public Policy
- EPS 1400 - Atmosphere, Ocean and Climate Change
- EPS 3120 - Structural Geology
- EVST 1000/APHY 1000/ENAS 1000/EPS 1050/PHYS 1000 - Energy, Environment, and Public Policy - Instructor Permission Required
- EVST 2206 - Sustainable Energy: Physics and History - Mathematical proficiency with algebra is assumed. Students from all academic interests and experiences are welcome in the course.
- GLBL 2121 - Applied Quantitative Analysis
- GLBL 2159/ECON 159 – Game Theory
- MATH 1030 - Mathematics of Voting - Permission of instructor required
- MATH 1070 – Mathematics in the Real World - Instructor Permission Required
- MATH 3300 - Advanced Probability - Some knowledge of real analysis assumed.
- PHIL 1115 - First Order Logic
- PHYS 1000/APHY 1000/ENAS 1000/EVST 1000 - Energy, Environment, and Public Policy - Instructor Permission Required
- PHYS 1060/EVST 206/HIST 127/HSHM 201/HUMS 106, Sustainable Energy: Physics and History
- PHYS 1710 - University Physics for Life Sciences - Concurrently with MATH 1150. See comparison of introductory sequences and laboratories in the YCPS.
- PHYS 2600 - Intensive Introductory Physics - Concurrently with MATH 1200, ENAS 1510, PHYS 1510, or PHYS 4000, or equivalent. Students considering an alternative MATH course should check with the DUS in Physics.
- PHYS 2610 - Intensive Introductory Physics - Concurrently with MATH 1200, ENAS 1501, PHYS 1510, or PHYS 4000, or equivalent. Students considering an alternative MATH course should check with the DUS in Physics.
- PHYS 3590 - Research Methods in Astrophysics Instructor Permission Required.
- S&DS 1230/CPSC 1230/PLSC 3508 – YData: An Introduction to Data Science
- S&DS 2200 - Introductory Statistics, Intensive - MATH 115 is helpful but not required. While no particular prior experience in computing is required, strong motivation to practice and learn computing are desirable.
- S&DS 4000/MATH 3300 - Advanced Probability