printer friendly pageMATH 177: Geometric Methods in the Theory of Ordinary Differential Equations
Hamiltonian systems and their geometry. First order PDE and Hamilton-Jacobi equation. Structural stability and hyperbolic dynamical systems. Completely integrable systems. Perturbation theory.
Last offered: Spring 2018
| UG Reqs: WAY-FR
MS&E 20: Discrete Probability Concepts And Models
Fundamental concepts and tools for the analysis of problems under uncertainty, focusing on structuring, model building, and analysis. Examples from legal, social, medical, and physical problems. Topics include axioms of probability, probability trees, belief networks, random variables, conditioning, and expectation. The course is fast-paced, but it has no prerequisites.
Terms: Sum
| Units: 4
| UG Reqs: WAY-FR
Instructors:
Shachter, R. (PI)
MS&E 120: Introduction to Probability
Probability is the foundation behind many important disciplines including statistics, machine learning, risk analysis, stochastic modeling and optimization. This course provides an in-depth undergraduate-level introduction to fundamental ideas and tools of probability. Topics include: the foundations (sample spaces, random variables, probability distributions, conditioning, independence, expectation, variance), a systematic study of the most important univariate and multivariate distributions (Normal, Multivariate Normal, Binomial, Poisson, etc...), as well as a peek at some limit theorems (basic law of large numbers and central limit theorem) and, time permitting, some elementary markov chain theory. Prerequisite:
CME 100 or
MATH 51.
Terms: Aut
| Units: 4
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR
MS&E 152: Introduction to Decision Analysis
How to make good decisions in a complex, dynamic, and uncertain world. People often make decisions that on close examination they regard as wrong. Decision analysis uses a structured conversation based on actional thought to obtain clarity of action in a wide variety of domains. Topics: distinctions, possibilities and probabilities, relevance, value of information and experimentation, relevance and decision diagrams, risk attitude. Prerequisites: high school algebra and basic spreadsheet skills.
Terms: Spr
| Units: 3-4
| UG Reqs: WAY-AQR, GER:DB-EngrAppSci, WAY-FR
Instructors:
Shachter, R. (PI)
;
Dai, Y. (TA)
;
Rodriguez Silva Santisteban, F. (TA)
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Instructors:
Shachter, R. (PI)
;
Dai, Y. (TA)
;
Rodriguez Silva Santisteban, F. (TA)
;
Wu, Z. (TA)
;
Zhao, Y. (TA)
OCEANS 143: Quantitative Methods for Marine Ecology and Conservation (BIO 143, BIO 243, CEE 164, CEE 264H, EARTHSYS 143H, EARTHSYS 243H)
NOTE: This course will be taught in-person on main campus, in hybrid format with Zoom options. The goal of this course is to learn the foundations of ecological modeling with a specific (but not exclusive) focus on marine conservation and sustainable exploitation of renewable resources. Students will be introduced to a range of methods - from basic to advanced - to characterize population structure, conduct demographic analyses, estimate extinction risk, identify temporal trends and spatial patterns, quantify the effect of environmental determinants and anthropogenic pressures on the dynamics of marine populations, describe the potential for adaptation to climate change. This course will emphasize learning by doing, and will rely heavily on practical computer laboratories, in R and/or Phyton, based on data from our own research activities or peer reviewed publications. Students with a background knowledge of statistics, programming and calculus will be most welcome. Formally
BIOHOPK 143H and 243H.
Terms: Win
| Units: 4
| UG Reqs: WAY-AQR, WAY-FR
Instructors:
De Leo, G. (PI)
;
Friedman, K. (TA)
OCEANS 174H: Experimental Design and Probability (OCEANS 274H)
Nature is inherently variable. Statistics gives us the tools to quantify the uncertainty of our measurements and draw conclusions from data. This course is an introduction to experimental design, probability, and data analysis. Topics include summary statistics, data visualization, probability distributions, statistical inference, and general linear models (e.g., t-tests, analysis of variance, regression). Students will use R to explore and analyze datasets relevant to the life and ocean sciences. No programming or statistical background is assumed. This course takes place in-person only at Hopkins Marine Station; for information on how to spend spring quarter in residence:
https://hopkinsmarinestation.stanford.edu/undergraduate-studies/spring-courses-23-24 (Individual course registration also permitted.) Depending on enrollment numbers, a weekly shuttle to Hopkins or mileage reimbursements for qualifying carpools will be provided; terms and conditions apply. Graduate students register for
OCEANS 274H.
Terms: Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-AQR, GER: DB-NatSci, WAY-FR
PHIL 49: Survey of Formal Methods
Survey of important formal methods used in philosophy. The course covers the basics of propositional and elementary predicate logic, probability and decision theory, game theory, and statistics, highlighting philosophical issues and applications. Specific topics include the languages of propositional and predicate logic and their interpretations, rationality arguments for the probability axioms, Nash equilibrium and dominance reasoning, and the meaning of statistical significance tests. Assessment is through a combination of problems designed to solidify competence with the mathematical tools and short-answer questions designed to test conceptual understanding.
Terms: Spr
| Units: 4
| UG Reqs: WAY-FR, GER:DB-Math
Instructors:
Bassett, R. (PI)
;
Forster, M. (TA)
PHIL 50S: Introduction to Formal Methods in Contemporary Philosophy
This course will serve as a first introduction to the formal tools and techniques of contemporary philosophy, including probability and formal logic. Traditionally, philosophy is an attempt to systematically tackle foundational problems related to value, inquiry, mind and reality. Contemporary philosophy continuesthis tradition of critical thinking with modern subject matter (often engaging with natural, social and mathematical science) and modern rigorous methods, including the methods of set theory, probability theory and formal logic. The aim of this course is to introduce such methods, along with various core philosophical distinctions and motivations. The focus will be on basic conceptual underpinnings and skills, not technical details. The material covered is also useful preparation for certain topics in mathematics, computer science, linguistics, economics and statistics. No previous philosophical or mathematical training is presupposed, though an appreciation of precise thinking is an advantage.
Last offered: Summer 2023
| UG Reqs: WAY-FR
PHIL 99: Minds and Machines (CS 24, LINGUIST 35, PSYCH 35, SYMSYS 1, SYMSYS 200)
(Formerly
SYMSYS 100). An overview of the interdisciplinary study of cognition, information, communication, and language, with an emphasis on foundational issues: What are minds? What is computation? What are rationality and intelligence? Can we predict human behavior? Can computers be truly intelligent? How do people and technology interact, and how might they do so in the future? Lectures focus on how the methods of philosophy, mathematics, empirical research, and computational modeling are used to study minds and machines. Students must take this course before being approved to declare Symbolic Systems as a major. All students interested in studying Symbolic Systems are urged to take this course early in their student careers. The course material and presentation will be at an introductory level, without prerequisites. If you have any questions about the course, please email symsys1staff@gmail.com.
Terms: Aut, Win, Sum
| Units: 4
| UG Reqs: GER:DB-SocSci, WAY-FR
Instructors:
Goodman, N. (PI)
;
Krejci, B. (PI)
;
Rose, D. (PI)
;
Wu, J. (PI)
;
Eigbe, N. (TA)
;
Fergesen, C. (TA)
;
Forster, M. (TA)
;
Graham, C. (TA)
;
Mon, K. (TA)
;
Ota, K. (TA)
;
Qing, C. (TA)
;
Ragupathi, A. (TA)
;
Schechtman, K. (TA)
;
Tong, N. (TA)
;
Xu, R. (TA)
PHIL 150: Mathematical Logic (PHIL 250)
An introduction to the concepts and techniques used in mathematical logic, focusing on propositional, modal, and predicate logic. Highlights connections with philosophy, mathematics, computer science, linguistics, and neighboring fields.
Terms: Aut
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Icard, T. (PI)
;
Apsel, L. (TA)
;
Bassett, R. (TA)
;
Thobani, I. (TA)
;
Tilton, S. (TA)
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