Search Results
Your search for courses · during 24FA, 25WI, 25SP · meeting requirements for FSR, Formal or Statistical Reasoning · returned 60 results
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BIOL 244 Biostatistics 3 credits
An introduction to statistical techniques commonly used in Biology. The course will use examples from primary literature to examine the different ways that biological data are organized and analyzed. Emphasis will be placed on how to choose the appropriate statistical techniques in different circumstances and how to use statistical software to carry out tests. Topics covered include variable types (categorical, parametric, and non-parametric), analysis of variance, generalized linear models, and meta-analysis. There will be an opportunity for students to analyze data from their own research experiences.
- Winter 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): BIOL 125 – Genes, Evolution, and Development & Lab with a grade of C- or better or received a score of 5 or better on the Biology AP exam or received a score of 6 or better on the Biology IB exam AND BIOL 126 – Energy Glow in Biological Systems & Lab with a grade of C- or better AND one 200 or 300 level BIOL course with a grade of C- or better.
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CS 111 Introduction to Computer Science 6 credits
This course will introduce you to computer programming and the design of algorithms. By writing programs to solve problems in areas such as image processing, text processing, and simple games, you will learn about recursive and iterative algorithms, complexity analysis, graphics, data representation, software engineering, and object-oriented design. No previous programming experience is necessary.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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NOT open to students who have completed any of the following course(s): CS 201 or greater with a grade of C- or better.
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CS 200 Data Structures with Problem Solving 6 credits
Think back to your favorite assignment from Introduction to Computer Science. Did you ever get the feeling that “there has to be a better/smarter way to do this problem”? The Data Structures course is all about how to store information intelligently and access it efficiently. How can Google take your query, compare it to billions of web pages, and return the answer in less than one second? How can one store information so as to balance the competing needs for fast data retrieval and fast data modification? To help us answer questions like these, we will analyze and implement stacks, queues, trees, linked lists, graphs, and hash tables. This version of Data Structures includes extra class time to support students’ problem solving by meeting five days per week, and is encouraged for students who may have struggled in CS111 or otherwise believe they would benefit from extra support. This course fulfills all requirements of CS 201, and students should take only one of CS 200 or CS 201.
Not open to students who have taken CS 201. This course meets 5 days a week
- Winter 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): CS 111 – Introduction to Computer Science with a grade of C- or better or a score of 4 or better on the Computer Science A AP exam or equivalent. Not open to students that have taken CS 201– Data Structures.
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CS 201 Data Structures 6 credits
Think back to your favorite assignment from Introduction to Computer Science. Did you ever get the feeling that “there has to be a better/smarter way to do this problem”? The Data Structures course is all about how to store information intelligently and access it efficiently. How can Google take your query, compare it to billions of web pages, and return the answer in less than one second? How can one store information so as to balance the competing needs for fast data retrieval and fast data modification? To help us answer questions like these, we will analyze and implement stacks, queues, trees, linked lists, graphs, and hash tables. Students who have received credit for a course for which Computer Science 201 is a prerequisite are not eligible to enroll in Computer Science 201.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): CS 111 – Introduction to Computer Science with a grade of C- or better or a score of 4 or better on the Computer Science A AP exam or equivalent. Not open to students that have taken CS 200 – Data Structures with Problem Solving.
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CS 202 Mathematics of Computer Science 6 credits
This course introduces some of the formal tools of computer science, using a variety of applications as a vehicle. You’ll learn how to encode data so that when you scratch the back of a DVD, it still plays just fine; how to distribute “shares” of your floor’s PIN so that any five of you can withdraw money from the floor bank account (but no four of you can); how to play chess; and more. Topics that we’ll explore along the way include: logic and proofs, number theory, elementary complexity theory and recurrence relations, basic probability, counting techniques, and graphs.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 111 – Introduction to Computer Science with a grade of C- or better or received a score of 4 or better on the AP Computer Science exam AND MATH 101 – Calculus with Problem Solving or MATH 111 – Introduction to Calculus or greater with a grade of C- or better or greater or received a score of 4 or better on the Calculus AB AP exam or received a score of 4 or better on the Calculus BC AP exam or received a score of 5 or better on the Mathematics IB exam or equivalent.
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CS 208 Introduction to Computer Systems 6 credits
Are you curious what’s really going on when a computer runs your code? In this course we will demystify the machine and the tools that we use to program it. Our broad survey of how computer systems execute programs, store information, and communicate will focus on the hardware/software interface, including data representation, instruction set architecture, the C programming language, memory management, and the operating system process model.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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CS 251 Programming Languages: Design and Implementation 6 credits
What makes a programming language like “Python” or like “Java”? This course will look past superficial properties (like indentation) and into the soul of programming languages. We will explore a variety of topics in programming language construction and design: syntax and semantics, mechanisms for parameter passing, typing, scoping, and control structures. Students will expand their programming experience to include other programming paradigms, including functional languages like Scheme and ML.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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CS 252 Algorithms 6 credits
A course on techniques used in the design and analysis of efficient algorithms. We will cover several major algorithmic design paradigms (greedy algorithms, dynamic programming, divide and conquer, and network flow). Along the way, we will explore the application of these techniques to a variety of domains (natural language processing, economics, computational biology, and data mining, for example). As time permits, we will include supplementary topics like randomized algorithms, advanced data structures, and amortized analysis.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures AND CS 202 – Mathematics of Computer Science or MATH 236 – Mathematical Structures with a grade of C- or better or equivalent. MATH 236 will be accepted in lieu of Computer Science 202.
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CS 254 Computability and Complexity 6 credits
An introduction to the theory of computation. What problems can and cannot be solved efficiently by computers? What problems cannot be solved by computers, period? Topics include formal models of computation, including finite-state automata, pushdown automata, and Turing machines; formal languages, including regular expressions and context-free grammars; computability and uncomputability; and computational complexity, particularly NP-completeness.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures AND CS 202 – Mathematics of Computer Science or MATH 236 – Mathematical Structures with a grade of C- or better or equivalent. MATH 236 will be accepted in lieu of Computer Science 202.
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CS 257 Software Design 6 credits
It’s easy to write a mediocre computer program, and lots of people do it. Good programs are quite a bit harder to write, and are correspondingly less common. In this course, we will study techniques, tools, and habits that will improve your chances of writing good software. While working on several medium-sized programming projects, we will investigate code construction techniques, debugging and profiling tools, testing methodologies, UML, principles of object-oriented design, design patterns, and user interface design.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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CS 304 Social Computing 6 credits
The last decade has seen a vast increase in the number of applications that connect people with one another. This course presents an interdisciplinary introduction to social computing, a field of study that explores how computational techniques and artifacts are used to support and understand social interactions. We will examine a number of socio-technical systems (such as wikis, social media platforms, and citizen science projects), discuss the design principles used to build them, and analyze how they help people mobilize and collaborate with one another. Assignments will involve investigating datasets from online platforms and exploring current research in the field.
- Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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CS 311 Computer Graphics 6 credits
Scientific simulations, movies, and video games often incorporate computer-generated images of fictitious worlds. How are these worlds represented inside a computer? How are they “photographed” to produce the images that we see? What performance constraints and design trade-offs come into play? In this course we learn the basic theory and methodology of three-dimensional computer graphics, including both triangle rasterization and ray tracing. Familiarity with vectors and matrices is recommended but not required.
- Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): CS 208 – Intro to Computer Systems with grade of C- or better.
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CS 314 Data Visualization 6 credits
Understanding the wealth of data that surrounds us can be challenging. Luckily, we have evolved incredible tools for finding patterns in large amounts of information: our eyes! Data visualization is concerned with taking information and turning it into pictures to better communicate patterns or discover new insights. It combines aspects of computer graphics, human-computer interaction, design, and perceptual psychology. In this course, we will learn the different ways in which data can be expressed visually and which methods work best for which tasks. Using this knowledge, we will critique existing visualizations as well as design and build new ones.
- Winter 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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CS 320 Machine Learning 6 credits
What does it mean for a machine to learn? Much of modern machine learning focuses on identifying patterns in large datasets and using these patterns to make predictions about the future. Machine learning has impacted a diverse array of applications and fields, from scientific discovery to healthcare to education. In this artificial intelligence-related course, we’ll both explore a variety of machine learning algorithms in different application areas, taking both theoretical and practical perspectives, and discuss impacts and ethical implications of machine learning more broadly. Topics may vary, but typically focus on regression and classification algorithms, including neural networks.
- Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures AND CS 202 – Mathematics of Computer Science or MATH 236 – Mathematical Structures with a grade of C- or better or equivalent. MATH 236 will be accepted in lieu of Computer Science 202.
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CS 321 Making Decisions with Artificial Intelligence 6 credits
There are many situations where computer systems must make intelligent choices, from selecting actions in a game, to suggesting ways to distribute scarce resources for monitoring endangered species, to a search-and-rescue robot learning to interact with its environment. Artificial intelligence offers multiple frameworks for solving these problems. While popular media attention has often emphasized supervised machine learning, this course instead engages with a variety of other approaches in artificial intelligence, both established and cutting edge. These include intelligent search strategies, game playing approaches, constrained decision making, reinforcement learning from experience, and more. Coursework includes problem solving and programming.
- Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures AND CS 202 – Mathematics of Computer Science or MATH 236 – Mathematical Structures with a grade of C- or better or equivalent. MATH 236 will be accepted in lieu of Computer Science 202.
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CS 322 Natural Language Processing 6 credits
Computers are poor conversationalists, despite decades of attempts to change that fact. This course will provide an overview of the computational techniques developed in the attempt to enable computers to interpret and respond appropriately to ideas expressed using natural languages (such as English or French) as opposed to formal languages (such as C++ or Lisp). Topics in this course will include parsing, semantic analysis, machine translation, dialogue systems, and statistical methods in speech recognition.
- Fall 2024
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures AND CS 202 – Mathematics of Computer Science or MATH 236 – Mathematical Structures with a grade of C- or better or equivalent. MATH 236 will be accepted in lieu of Computer Science 202.
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CS 330 Introduction to Real-Time Systems 6 credits
How can we prove that dynamic cruise control will brake quickly enough if traffic suddenly stops? How must a system coordinate processes to detect pedestrians and other vehicles to ensure fair sharing of computing resources? In real-time systems, we explore scheduling questions like these, which require provable guarantees of timing constraints for applications including autonomous vehicles. This course will start by considering such questions for uniprocessor machines, both when programs have static priorities and when priorities can change over time. We will then explore challenges introduced by modern computers with multiple processors. We will consider both theoretical and practical perspectives.
- Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures AND CS 202 – Mathematics of Computer Science or MATH 236 – Mathematical Structures with a grade of C- or better or equivalent. MATH 236 will be accepted in lieu of Computer Science 202.
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CS 338 Computer Security 6 credits
When hackers can disable gas pipelines, national hospital systems, and electrical grids, and data brokers can create a largely unregulated world-wide surveillance system, there’s a clear need for people who understand the mechanisms of computer security and insecurity. Towards that end, in this course we will study technical and social aspects of computer and network security. Topics will include threat modeling, cryptography, secure network protocols, web security, ethical hacking and penetration testing, authentication, authorization, historical hacking incidents, usability, privacy, and security-related law.
- Fall 2024
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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CS 344 Human-Computer Interaction 6 credits
The field of human-computer interaction addresses two fundamental questions: how do people interact with technology, and how can technology enhance the human experience? In this course, we will explore technology through the lens of the end user: how can we design effective, aesthetically pleasing technology, particularly user interfaces, to satisfy user needs and improve the human condition? How do people react to technology and learn to use technology? What are the social, societal, health, and ethical implications of technology? The course will focus on design methodologies, techniques, and processes for developing, testing, and deploying user interfaces.
- Winter 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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CS 347 Advanced Software Design 6 credits
This course helps students to strengthen their ability to design modular, extensible and maintainable software. The focus of the course is on the design of modern cloud applications. Students will learn how to decompose complex applications into a set of back-end services, develop and debug these services, and deploy them in the cloud. This class is structured around a large project that will be extended over the course of the term.
- Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS – 257 – Software Design with a grade of C- or better or equivalent.
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CS 348 Parallel and Distributed Computing 6 credits
As multi-core machines become more prevalent, different programming paradigms have emerged for harnessing extra processors for better performance. This course explores parallel computation for both shared memory and distributed parallel programming paradigms. In particular, we will explore how these paradigms affect the code we write, the libraries we use, and the advantages and disadvantages of each. Topics will include synchronization primitives across these models for parallel execution, debugging concurrent programs, fork/join parallelism, example parallel algorithms, computational complexity and performance considerations, computer architecture as it relates to parallel computation, and related theory topics.
- Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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CS 361 Artificial Life and Digital Evolution 6 credits
The field of artificial life seeks to understand the dynamics of life by separating them from the substrate of DNA. In this course, we will explore how we can implement the dynamics of life in software to test and generate biological hypotheses, with a particular focus on evolution. Topics will include the basic principles of biological evolution, transferring experimental evolution techniques to computational systems, cellular automata, computational modeling, and digital evolution. All students will be expected to complete and present a term research project recreating and extending recent work in the field of artificial life.
- Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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CS 364 Computational Modeling and Simulation of Natural Systems 6 credits
Computational models have become a fundamental part of how we make sense of the world, doing everything from economic forecasting to simulating the birth of the universe. But we need to understand how to use models effectively. In this class we’ll explore computational models used across many disciplines, including: agent-based models to prevent forest fires, compartmental models to protect endangered species, N-body models to track the spread of germs from a sneeze, and more. We’ll learn about what problems are (and are not) suited for computational modeling and engage with extensive datasets to evaluate and refine models for practical use.
- Fall 2024
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): CS 200 – Data Structures with Problem Solving or CS 201 – Data Structures with a grade of C- or better or equivalent.
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DGAH 220 Creative Coding and Generative AI 6 credits
Generative AI tools such as ChatGPT and GitHub CoPilot are fundamentally reshaping programming practices and workflows, raising questions about the future of code and so-called "prompt engineering," or writing for the machine. This class will situate this moment of potential transformation in the history of literate programming and "natural language" coding using Inform 7, as well as current tools such as ml5.js, an accessible machine learning library. Students will engage this history and future of computational creativity through writing and re-writing code, both with and without generative AI interventions, for conversational bots, interactive fiction, and experimental games.
- Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): CS 111 – Introduction to Computer Science with a grade of C- or better or a score of 4 or better on the Computer Science A AP exam or equivalent.
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ENTS 232 Research Methods in Environmental Studies 3 credits
This course covers various methodologies that are used to prosecute interdisciplinary academic research relating to the environment. Among the topics covered are: identification of a research question, methods of analysis, hypothesis testing, and effective rhetorical methods, both oral and written.
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LING 110 Introduction to Linguistics 6 credits
The capacity to acquire and use natural languages such as English is surely one of the more remarkable features of human nature. In this course, we explore several aspects of this ability. Topics include the sound systems of natural languages, the structure of words, principles that regulate word order, the course of language acquisition in children, and what these reveal about the nature of the mind.
- Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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LING 115 Introduction to the Theory of Syntax 6 credits
This course is organized to enable the student to actively participate in the construction of a rather elaborate theory of the nature of human cognitive capacity to acquire and use natural languages. In particular, we concentrate on one aspect of that capacity: the unconscious acquisition of a grammar that enables a speaker of a language to produce and recognize sentences that have not been previously encountered. In the first part of the course, we concentrate on gathering notation and terminology intended to allow an explicit and manageable description. In the second part, we depend on written and oral student contributions in a cooperative enterprise of theory construction.
- Fall 2024, Spring 2025
- FSR, Formal or Statistical Reasoning
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LING 216 Generative Approaches to Syntax 6 credits
This course has two primary goals: to provide participants with a forum to continue to develop their analytical skills (i.e., to ‘do syntax’), and to acquaint them with generative syntactic theory, especially the Principles and Parameters approach. Participants will sharpen their technological acumen, through weekly problem solving, and engage in independent thinking and analysis, by means of formally proposing novel syntactic analyses for linguistic phenomena. By the conclusion of the course, participants will be prepared to read and critically evaluate primary literature couched within this theoretical framework.
- Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has completed LING 115 – Intro to the Theory of Syntax with grade of C- or better
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LING 217 Phonetics and Phonology 6 credits
Although no two utterances are ever exactly the same, we humans don’t function like tape recorders; we overlook distinctions to which mechanical recording devices are sensitive, and we “hear” contrasts which are objectively not there. What we (think we) hear is determined by the sound system of the language we speak. This course examines the sound systems of human languages, focusing on how speech sounds are produced and perceived, and how these units come to be organized into a systematic network in the minds of speakers of languages.
- Fall 2024
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): One 100-level LING course with grade of C- or better.
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LING 315 Topics in Syntax 6 credits
What moves where, how, and for what purpose? In this course, participants explore accounts of various types of syntactic movement within the Minimalist Program. After an introduction to Minimalism, we read, discuss, and evaluate primary literature. This course offers an overview of the progression of generative syntactic theory from the mid-1980s to the mid-1990s, with a focus on objectively comparing competing analyses. By the end of the course, participants will have familiarity with scholarly literature on theoretical syntax; with evaluating and critiquing existing theoretical analyses; and with proposing and defending a novel analysis.
- Fall 2024
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): LING 216 – Generative Approach to Syntax with grade of C- or better.
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MATH 101 Calculus with Problem Solving 6 credits
An introduction to the central ideas of calculus with review and practice of those skills needed for the continued study of calculus. Problem solving strategies will be emphasized. In addition to regular MWF class time, students will be expected to attend two problem-solving sessions each week, one on Monday or Tuesday, and one on Wednesday or Thursday. Details will be provided on the first day of class.
Extra time for TTH labs. Not open to students who have received credit for MATH 111
- Fall 2024, Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has received a score of 101 on the Carleton Math Placement exam. Not open to students who have received credit for Mathematics 111. For more information, see the Mathematics' web page.
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MATH 111 Introduction to Calculus 6 credits
An introduction to the differential and integral calculus. Derivatives, antiderivatives, the definite integral, applications, and the fundamental theorem of calculus.
Not open to students who have received credit for MATH 101
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has received a score of 111 on the Carleton Math Placement exam. Not open to students who have received credit for Mathematics 101 or received a score of 4 or better on the Calculus AB AP exam or received a score of 4 or better on the Calculus BC AP exam or received a score of 5 or better on the Calculus IB exam. For more information, see the Mathematics' web page.
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MATH 120 Calculus 2 6 credits
Inverse functions, integration by parts, improper integrals, modeling with differential equations, vectors, calculus of functions of two independent variables including directional derivatives and double integrals, Lagrange multipliers.
Not open to students who have received credit for MATH 211 or have a score of 4 or 5 on the AP Calculus BC exam.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 101 – Calculus with Problem Solving or MATH 111 – Introduction to Calculus with a grade of C- or better or received a scored of 4 or better on AP Calculus AB test or received a scored of 5 or better on Calculus IB test or placement exam. Not open to students who received a scored of 4 or better on the AP Calculus BC test or completed MATH 211 with a grade of C- or better.
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MATH 134 Linear Algebra with Applications 6 credits
Linear algebra centers on the geometry, algebra, and applications of linear equations. It is pivotal to many areas of mathematics, natural sciences, computer science, and engineering. To study linear equations, we will develop concepts including matrix algebra, linear independence, determinants, eigenvectors, and orthogonality. Students will use these tools to model real world problems and solve these problems using computational software.
This course is not open to students who have received credit for MATH 232.
- Fall 2024, Spring 2025
- FSR, Formal or Statistical Reasoning
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Not open to students who have taken MATH 232 – Linear Algebra or equivalents.
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MATH 210 Calculus 3 6 credits
Vectors, curves, calculus of functions of three independent variables, including directional derivatives and triple integrals, cylindrical and spherical coordinates, line integrals, Green's theorem, sequences and series, power series, Taylor series. This course cannot be substituted for MATH 211.
This course cannot be substituted for MATH 211
- Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 120 – Calculus 2 with a grade of C- or better. Students who have received a score of 4 or greater on the AP Calculus BC exam should register for MATH 211 – Multivariable Calculus.
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MATH 211 Introduction to Multivariable Calculus 6 credits
Vectors, curves, partial derivatives, gradient, multiple and iterated integrals, line integrals, Green’s theorem.
- Fall 2024, Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has received a score of 4 or better on the AP Calculus BC exam or received a score of 211 on the Carleton Math Placement exam.
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MATH 232 Linear Algebra 6 credits
Linear algebra centers on the study of highly structured functions called linear transformations. Given the abundance of nonlinear functions in mathematics, it may come as a surprise that restricting to linear ones opens the door to a rich and powerful theory that finds applications throughout mathematics, statistics, computer science, and the natural and social sciences. Linear transformations are everywhere, once we know what to look for. They appear in calculus as the functions that are used to define lines and planes in Euclidean space. In fact, differentiation is also a linear transformation that takes one function to another. The course focuses on developing geometric intuition as well as computational matrix methods. Topics include kernel and image of a linear transformation, vector spaces, determinants, eigenvectors and eigenvalues.
This course is not open to students who have received credit for MATH 134.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 120 – Calculus 2 or MATH 211 – Introduction to Multivariable Calculus with a grade of C- or better or equivalent.
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MATH 236 Mathematical Structures 6 credits
Basic concepts and techniques used throughout mathematics. Topics include logic, mathematical induction and other methods of proof, problem solving, sets, cardinality, equivalence relations, functions and relations, and the axiom of choice. Other topics may include: algebraic structures, graph theory, and basic combinatorics.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 134 – Linear Algebra with Applications or MATH 232– Linear Algebra AND MATH 210 – Calculus 3 or MATH 211 – Multivariable Calculus with a grade of C- or better or equivalent.
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MATH 240 Probability 6 credits
Introduction to probability and its applications. Topics include discrete probability, random variables, independence, joint and conditional distributions, expectation, limit laws and properties of common probability distributions.
- Fall 2024, Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 120 – Calculus 2 or MATH 211 – Introduction to Multivariable Calculus or greater with a grade of C- or better or received a score of 4 or better on the Calculus BC AP exam or equivalent.
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MATH 241 Ordinary Differential Equations 6 credits
Ordinary differential equations are a fundamental language used by mathematicians, scientists, and engineers to describe processes involving continuous change. In this course we develop ordinary differential equations as models of real world phenomena and explore the mathematical ideas that arise within these models. Topics include separation of variables; phase portraits; equilibria and their stability; non-dimensionalization; bifurcation analysis; and modeling of physical, biological, chemical, and social processes.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student must have completed any of the following course(s): MATH 134 – Linear Algebra with Applications or MATH 232 – Linear Algebra AND MATH 120 – Calculus 2 or MATH 211 – Multivariable Calculus with a grade of C- or better or equivalents.
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MATH 251 Chaotic Dynamics 6 credits
Dynamics is the branch of mathematics that deals with the study of change. In this course we will focus on simple discrete non-linear dynamical systems that produce astoundingly rich and unpredictable behavior — something that is colloquially referred to as "chaos". Topics will include one dimensional dynamics (including fixed points and their classifications), Sharkovsky's Theorem, a careful formulation/definition of "chaos", symbolic dynamics, complex dynamics (including Julia and Mandelbrot sets), iterated function systems, fractals and more.
- Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C- or better or equivalent.
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MATH 271 Optimization 6 credits
Optimization is all about selecting the "best" thing. Finding the most likely strategy to win a game, the route that gets you there the fastest, or the curve that most closely fits given data are all examples of optimization problems. In this course we study linear optimization (also known as linear programming), the simplex method, and duality from both a theoretical and a computational perspective. Applications will be selected from statistics, economics, computer science, and more. Additional topics in nonlinear and convex optimization will be covered as time permits.
- Spring 2025
- FSR, Formal or Statistical Reasoning
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Student must have completed any of the following course(s): MATH 134 – Linear Algebra with Applications or MATH 232 – Linear Algebra AND MATH 120 – Calculus 2 or MATH 211 – Multivariable Calculus with a grade of C- or better or equivalents.
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MATH 295.00 Numerical Differential Equations 6 credits
An introduction to numerical methods to compute approximate solutions of differential equations. Material will be selected from a range of topics such as error analysis, numerical differentiation, Euler and Runge-Kutta methods, predictor-corrector methods, boundary value problems, and curve fitting. Applications to other subjects such as physics, chemistry, ecology, epidemiology and neuroscience will be covered. Programming experience is not required.
- Fall 2024
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): MATH 134 – Linear Algebra with Applications or MATH 232 – Linear Algebra with a grade of C- or better or equivalent.
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MATH 321 Real Analysis I 6 credits
A systematic study of single-variable functions on the real numbers. This course develops the mathematical concepts and tools needed to understand why calculus really works: the topology of the real numbers, limits, differentiation, integration, convergence of sequences, and series of functions.
- Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 – Mathematical Structures AND MATH 210 – Calculus 3 or MATH 211 – Multivariable Calculus with a grade of C- or better or equivalents.
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MATH 331 Real Analysis II 6 credits
Further topics in analysis such as measure theory, Lebesgue integration or Banach and Hilbert spaces.
- Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 321 – Real Analysis I with a grade of C- or better.
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MATH 333 Combinatorial Theory 6 credits
The study of structures involving finite sets. Counting techniques, including generating functions, recurrence relations, and the inclusion-exclusion principle; existence criteria, including Ramsey’s theorem and the pigeonhole principle. Some combinatorial identities and bijective proofs. Other topics may include graph and/or network theory, Hall’s (“marriage”) theorem, partitions, and hypergeometric series.
- Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C- or better or equivalent.
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MATH 341 Partial Differential Equations 6 credits
An introduction to partial differential equations with emphasis on the heat equation, wave equation, and Laplace’s equation. Topics include the method of characteristics, separation of variables, Fourier series, Fourier transforms and existence/uniqueness of solutions.
- Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 241 – Ordinary Differential Equations with grade of C- or better.
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MATH 342 Abstract Algebra I 6 credits
Introduction to algebraic structures, including groups, rings, and fields. Homomorphisms and quotient structures, polynomials, unique factorization. Other topics may include applications such as Burnside’s counting theorem, symmetry groups, polynomial equations, or geometric constructions.
- Fall 2024, Spring 2025
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C- or better or equivalent.
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MATH 344 Differential Geometry 6 credits
Differential geometry is the study of shapes (like curves and surfaces) using tools from linear algebra and calculus. In this course we focus on the differential geometry of curves and surfaces and the concepts of curvature, geodesics, and first and second fundamental forms. These concepts will lead us to remarkable results like the Theorem Egregium and the Gauss-Bonnet Theorem, which relate the ways that curvature and shape interact.
- Fall 2024
- FSR, Formal or Statistical Reasoning
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Student has completed any of the following course(s): MATH 236 – Mathematical Structures with a grade of C- or better or equivalent.
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MATH 395.01 Introduction to Analytic Number Theory 6 credits
An introduction to the techniques and principles of analytic number theory. Topics covered include arithmetical functions, Dirichlet multiplication, averages of arithmetical functions, elementary theorems on the distribution of the primes, and Dirichlet's theorem on primes in arithmetic progressions.
- Winter 2025
- FSR, Formal or Statistical Reasoning
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Student has completed the following course(s): MATH 321 – Real Analysis I and MATH 342 – Abstract Algebra I with a grade of C- or better.
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PHIL 210 Logic 6 credits
The study of formal logic has obvious and direct applicability to a wide variety of disciplines (including mathematics, computer science, linguistics, philosophy, cognitive science, and many others). Indeed, the study of formal logic helps us to develop the tools and know-how to think more clearly about arguments and logical relationships in general; and arguments and logical relationships form the backbone of any rational inquiry. In this course we will focus on propositional logic and predicate logic, and look at the relationship that these have to ordinary language and thought.
- Spring 2025
- FSR, Formal or Statistical Reasoning
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PSYC 200 Measurement and Data Analysis in Psychology 6 credits
The course considers the role of measurement and data analysis focused on behavioral sciences. Various forms of measurement and standards for the evaluation of measures are explored. Students learn how to summarize, organize, and evaluate data using a variety of techniques that are applicable to research in psychology and other disciplines. Among the analyses discussed and applied are tests of means, various forms of analysis of variance, correlation and regression, planned and post-hoc comparisons, as well as various non-parametric tests. Research design is also explored.
- Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): PSYC 110 – Principles of Psychology with a grade of C- OR CGSC/PSYC 232 – Cognitive Processes and CGSC/PSYC 233 – Laboratory Cognitive Processes with a grade of C- or better or received a score of 4 or better on the Psychology AP exam or received a score of 6 or better on the Psychology IB exam.
- PSYC 201
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STAT 120 Introduction to Statistics 6 credits
Introduction to statistics and data analysis. Practical aspects of statistics will be emphasized, including extensive use of programming in the statistical software R, interpretation and communication of results. Topics include: exploratory data analysis, correlation and linear regression, design of experiments, the normal distribution, randomization approach to inference, sampling distributions, estimation, and hypothesis testing. Students who have taken Mathematics 211 are encouraged to consider the more advanced Mathematics 240/Statistics 250 Probability/Statistical Inference sequence.
Not open to students who have already received credit for Psychology 200/201, Sociology/Anthropology 239 or Statistics 250
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Not open to students that have taken PSYC 200 – Measurement and Data Analysis in Psychology, PSYC 201 – Measurement and Data Analysis Lab , SOAN 239 – Social Statistics or STAT 250 – Introduction to Statistical Inference.
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STAT 220 Introduction to Data Science 6 credits
This course will cover the computational side of data analysis, including data acquisition, management, and visualization tools. Topics may include: data scraping, data wrangling, data visualization using packages such as ggplots, interactive graphics using tools such as Shiny, an introduction to classification methods, and understanding and visualizing spatial data. We will use the statistics software R in this course.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): STAT 120 – Introduction to Statistics or STAT 230 – Applied Regression Analysis, or STAT 250 – Introduction to Statistical Inference with a grade of C- or better.
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STAT 230 Applied Regression Analysis 6 credits
A second course in statistics covering simple linear regression, multiple regression and ANOVA, and logistic regression. Exploratory graphical methods, model building and model checking techniques will be emphasized with extensive use of statistical software R to analyze real-life data.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): STAT 120 – Introduction to Statistics or STAT 250 – Introduction to Statistical Inference or PSYC 200 – Measurement & Data Analysis or SOAN 239 – Social Statistics with a grade of C- or better or received a score of 4 or better on the Statistics AP exam.
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STAT 250 Introduction to Statistical Inference 6 credits
Introduction to modern mathematical statistics. The mathematics underlying fundamental statistical concepts will be covered as well as applications of these ideas to real-life data. Topics include: resampling methods (permutation tests, bootstrap intervals), classical methods (parametric hypothesis tests and confidence intervals), parameter estimation, goodness-of-fit tests, regression, and Bayesian methods. The statistical package R will be used to analyze data sets.
- Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): MATH 240 – Probability with a grade of C- or better.
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STAT 270 Statistical Learning 6 credits
Statistical learning (sometimes called statistical machine learning) centers on the discovery of structural patterns and making predictions using complex data sets. This course explores supervised and unsupervised statistical learning methods, and the ethical considerations of their use. Topics may include nonparametric regression, classification, cross validation, linear model selection techniques and regularization, and clustering. Students will implement these concepts using open-source computational tools, such as the R language.
Not open to students who have received credit for CS 320
- Fall 2024
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): STAT 230 Applied Regression Analysis with a grade of C- or better and has NOT taken CS 320 – Machine Learning
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STAT 285 Statistical Consulting 2 credits
Students will apply their statistical knowledge by analyzing data problems solicited from the Northfield community. Students will also learn basic consulting skills, including communication and ethics.
All interested students are encouraged to add to the waitlist and the instructor will reach out after registration. This course is repeatable, but if the instructor cannot admit every student on the waitlist, priority will be given first to Statistics majors who have not previously taken the course and then to other students who have not taken the course.
- Fall 2024, Winter 2025, Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed the following course(s): STAT 230 – Applied Regression Analysis with a grade of C- or better.
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STAT 320 Time Series Analysis 6 credits
Models and methods for characterizing dependence in data that are ordered in time. Emphasis on univariate, quantitative data observed over evenly spaced intervals. Topics include perspectives from both the time domain (e.g., autoregressive and moving average models, and their extensions) and the frequency domain (e.g., periodogram smoothing and parametric models for the spectral density). Exposure to matrix algebra may be helpful but is not required.
- Spring 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): STAT 230 – Applied Regression Analysis and STAT 250 – Introduction to Statistical Inference with a grade of C- or better.
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STAT 330 Advanced Statistical Modeling 6 credits
Topics include linear mixed effects models for repeated measures, longitudinal or hierarchical data and generalized linear models (of which logistic and Poisson regression are special cases) including zero-inflated Poisson models. Depending on time, additional topics could include survival analysis or generalized additive models.
- Winter 2025
- FSR, Formal or Statistical Reasoning QRE, Quantitative Reasoning
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Student has completed any of the following course(s): STAT 230 – Applied Regression Analysis and STAT 250 – Introduction to Statistical Inference with a grade of C- or better and has completed or is in the process of completing MATH 134 – Linear Algebra with Practical Applications or MATH 232 – Linear Algebra with a grade of C- or better or equivalents.