MATH 120: Groups and Rings
Groups acting on sets, examples of finite groups, Sylow theorems, solvable and simple groups. Fields, rings, and ideals; polynomial rings over a field; PID and non-PID. Unique factorization domains. WIM.
Terms: Aut, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Galatius, S. (PI)
;
Soundararajan, K. (PI)
MATH 171: Fundamental Concepts of Analysis
Recommended for Mathematics majors and required of honors Mathematics majors. Similar to 115 but altered content and more theoretical orientation. Properties of Riemann integrals, continuous functions and convergence in metric spaces; compact metric spaces, basic point set topology. Prerequisite: 51H or 115 or consent of the instructor. WIM
Terms: Aut, Spr
| Units: 3
| UG Reqs: GER:DB-Math, WAY-FR
Instructors:
Galatius, S. (PI)
;
Simon, L. (PI)
MS&E 20: Discrete Probability Concepts And Models
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.
Terms: Sum
| Units: 3
| UG Reqs: WAY-FR
Instructors:
Shachter, R. (PI)
MS&E 120: Probabilistic Analysis
Concepts and tools for the analysis of problems under uncertainty, focusing on model building and communication: structuring, processing, and presentation of probabilistic information. Examples from legal, social, medical, and physical problems. Spreadsheets illustrate and solve problems as a complement to analytical closed-form solutions. Topics: axioms of probability, probability trees, random variables, distributions, conditioning, expectation, change of variables, and limit theorems. Prerequisite:
MATH 51. Recommended: knowledge of spreadsheets.
Terms: Aut
| Units: 5
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR
Instructors:
Shachter, R. (PI)
MS&E 152: Introduction to Decision Analysis (MS&E 152W)
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. Students seeking to fulfill the Writing in the Major requirement should register for MS&E 152W.
Terms: Spr
| Units: 3-4
| UG Reqs: WAY-AQR, GER:DB-EngrAppSci, WAY-FR
Instructors:
Shachter, R. (PI)
MS&E 152W: Introduction to Decision Analysis (MS&E 152)
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. Students seeking to fulfill the Writing in the Major requirement should register for MS&E 152W.
Terms: Spr
| Units: 3-4
| UG Reqs: WAY-AQR, GER:DB-EngrAppSci, WAY-FR
Instructors:
Shachter, R. (PI)
PHIL 50: Introductory Logic
Propositional and predicate logic; emphasis is on translating English sentences into logical symbols and constructing derivations of valid arguments.
Terms: Aut, Spr
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
PHIL 150: Basic Concepts in Mathematical Logic (PHIL 250)
(Formerly 159.) The concepts and techniques used in mathematical logic, primarily through the study of the language of first order logic. Topics: formalization, proof, propositional logic, quantifiers, sets, mathematical induction, and enumerability.
Terms: Aut
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
PHIL 150E: Logic in Action: A New Introduction to Logic
A new introduction to logic, covering propositional, modal, and first-order logic. Highlights connections with philosophy, mathematics, computer science, linguistics, and neighboring fields. Based on the open source logic course 'Logic in Action,' available online at
http://www.logicinaction.org/.nnFulfills the undergraduate philosophy logic requirement.
Terms: Spr
| Units: 4
| UG Reqs: WAY-FR, GER:DB-Math
PHIL 151: First-Order Logic (PHIL 251)
(Formerly 160A.) The syntax and semantics of sentential and first-order logic. Concepts of model theory. Gödel's completeness theorem and its consequences: the Löwenheim-Skolem theorem and the compactness theorem. Prerequisite: 150 or consent of instructor.
Terms: Win
| Units: 4
| UG Reqs: GER:DB-Math, WAY-FR
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