## Quantitative Reasoning

Last updated: August 28, 2019 at 2:18 PM

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Objectives

The quantitative reasoning requirement has been established to develop students' abilities to collect, summarize and analyze numerical data; to make abstract concepts operational; and to think critically about the accuracy and soundness of conclusions based on data or on mathematical models. Quantitative reasoning courses usually embed methodological training in their subject matter.

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Undergraduate Degree Requirement

Courses that satisfy the requirement in a particular semester are designated "qr" in the Schedule of Classes for that semester. Students must satisfactorily complete one quantitative reasoning course. Some courses satisfy the quantitative reasoning requirement only when they are taken with the corresponding lab.

### Courses of Instruction

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Quantitative Reasoning

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BCHM
100a
Advanced Introductory Biochemistry
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*Prerequisite: One year of organic chemistry with laboratory. *

Topics include protein and nucleic acid structure; chemical basis of enzyme-catalyzed reaction mechanisms and enzyme kinetics; the chemical logic of metabolic pathways, including glycolysis and oxidative phosphorylation; and regulation of enzymatic pathways through allosteric control. Usually offered every year in multiple sections.

Emily Westover

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BIOL
14a
Genetics and Genomics
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Studies fundamentals of genetics, molecular biology and genomics through analytical thinking and problem-solving. Topics include heredity, meiosis, molecular basis of phenotypic variations, and an introduction to tools and techniques used by past and current researchers in genetics. Usually offered every semester.

Rachel Woodruff

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BIOL
16a
Evolution and Biodiversity
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"Nothing in biology makes sense except in the light of evolution," the geneticist Theodosius Dobzhansky said famously. Evolution is the unifying theory of biology because it explains both the unity and diversity of life. This course examines processes and patterns of evolution, including the sources and fate of variation, natural selection and genetic drift, species and speciation, biogeography, and the history and diversity of life on Earth. We end with a discussion of human evolution and the impact we are having on the planet. Usually offered every fall.

James Morris

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BIOL
107a
Data Analysis and Statistics Workshop
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The interpretation of data is key to making new discoveries, making optimal decisions, and designing experiments. Students will learn skills of data analysis and computer coding through hands-on, computer-based tutorials and exercises that include experimental data from the biological sciences. Knowledge of very basic statistics (mean, median) will be assumed. Usually offered every year.

Stephen Van Hooser

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BUS
51a
Introduction to Data Analytics with Excel
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*Prerequisite: Bus 6a. May not be taken for credit by students who took BUS 51b in prior years.*

Teaches students how to analyze data, how to create data visualizations, and how to use data for basic inference. The course is taught using Microsoft Excel, thus allowing students to also learn the most common piece of software used in the workplace to analyze business data. Usually offered every semester.

Shawn Bhimani

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CHEM
11a
General Chemistry I
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*This course may not be taken for credit by students who have passed CHEM 15a in previous years. Four class hours and one sixty-minute structured study group session per week. The corresponding lab is CHEM 18a. *

Covers a wide array of topics, embracing aspects of descriptive, as well as quantitative, chemistry. No prior study of chemistry is assumed, as the course begins by looking at the atomic foundation of matter, the elements, and the organization of the periodic table, working its way up to studying how atoms are bonded together to form larger units of matter. Students who complete this course will have an understanding of the three major phases of matter—solids, liquids, and gases—and how they behave, as well as a knowledge of the major types of chemical reactions and how to represent them. A strong focus is put on learning methods of creative problem-solving—using the material as a way to develop creative approaches to solving unfamiliar problems—a skill that carries students far beyond the confines of the classroom. Usually offered every year.

Claudia Novack

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CHEM
11b
General Chemistry II
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*Prerequisite: A satisfactory grade (C- or better) in CHEM 11a or an approved equivalent. This course may not be taken for credit by students who have passed CHEM 15b in previous years. Four class hours and one sixty-minute structured study group session per week. The corresponding lab is CHEM 18b.*

Picks up where Chemistry 11a left off, advancing students’ understanding of bonding models and molecular structure and exploring the basics of coordination chemistry. Three major quantitative topics are covered in the second half of General Chemistry—chemical equilibrium (including acid-base chemistry, solubility, and complex-ion formation), chemical kinetics, and thermodynamics. Other topics explored are electrochemistry and nuclear chemistry. Usually offered every year.

Claudia Novack

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CHEM
15a
Honors General Chemistry I
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*This course may not be taken for credit by students who have passed CHEM 11a in previous years. Three class hours and one recitation per week. The corresponding laboratory is CHEM 19a.*

An advanced version of general chemistry for students with good preparation in math and chemistry in high school. Topics include chemical stoichiometry, chemical bonding from a classical and quantum mechanical perspective, gases, thermochemistry, solutions, states of matter atomic structure and periodic properties. Real world examples are used to demonstrate the concepts. Usually offered every year.

Rebecca Gieseking

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CHEM
15b
Honors General Chemistry II
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*Prerequisite: A satisfactory grade (C- or better) in CHEM 15a or the equivalent. This course may not be taken for credit by students who have passed CHEM 11b in previous years. Three class hours and one recitation per week. The corresponding laboratory is CHEM 19b.*

A continuation of CHEM 15a. Topics include an introduction to thermodynamics, chemical equilibria, including acid-base and solubility equilibria, electrochemistry, chemical kinetics, nuclear chemistry, coordination chemistry and special topics. Usually offered every year.

Klaus Schmidt-Rohr

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COSI
29a
Discrete Structures
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Covers topics in discrete mathematics with applications within computer science. Some of the topics to be covered include graphs and matrices; principles of logic and induction; number theory; counting, summation, and recurrence relations; discrete probability. Usually offered every year.

Staff

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COSI
123a
Statistical Machine Learning
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*Prerequisite: COSI 29a, MATH 10a, and MATH 15a.*

Focuses on learning from data using statistical analysis tools and deals with the issues of designing algorithms and systems that automatically improve with experience. This course is designed to give students a thorough grounding in the methodologies, technologies, mathematics, and algorithms currently needed by research in learning with data. Usually offered every year.

Pengyu Hong

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ECON
2a
A Survey of Economics
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*Intended for students who are not Economics majors or minors. May not be taken for credit by students who took ECON 10a in prior years.*

Introduces economic analysis with policy applications. The economist's approach to social analysis is systematically elaborated. Usually offered every semester.

Geoff Clarke

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ECON
10a
Introduction to Microeconomics
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*Intended for Economics majors and minors or students who intend to take more than one Economics course. Students who have taken ECON 2a and received a B+ or better cannot receive credit for this course. May not be taken for credit by students concurrently with or after they have taken ECON 80a.*

Introduces the field of microeconomics, which is the study of how individuals and firms make decisions and how these decisions interact. Usually offered every semester.

Geoff Clarke and Nelson Sa

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ECON
83a
Statistics for Economic Analysis
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*Prerequisite: ECON 2a or 10a. Students must earn a C- or higher in MATH 10a, or otherwise satisfy the calculus requirement, to enroll in this course.*

A first course in statistical inference. Topics include descriptive statistics, probability, normal and binomial distributions, sampling distributions, point and interval estimation, properties of estimators, hypothesis testing, regression, and analysis of variance. Usually offered every semester.

Linda Bui, Nidhiya Menon, and Tymon Słoczyński

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ECON
135a
Industrial Organization
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*Prerequisites: ECON 80a and ECON 83a or permission of the instructor.*

Microeconomic analysis of firm behavior under alternative market structures and implications for market outcomes. Topics include strategic interaction, entry and exit, collusion, predation, price discrimination, product differentiation, vertical relations, imperfect information, advertising, and patents and innovation. Usually offered every year.

Kathryn Graddy and Benjamin Shiller

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ECON
184b
Econometrics
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*Prerequisites: ECON 83a. Corequisite: ECON 80a or permission of the instructor. Students must earn a C- or higher in MATH 10a, or otherwise satisfy the calculus requirement, to enroll in this course. This course may not be taken for credit by students who have previously taken or are currently enrolled in ECON 185a or ECON 311a.*

An introduction to the theory of econometric regression and forecasting models, with applications to the analysis of business and economic data. Usually offered every year.

Elizabeth Brainerd and Joshua Goodman

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FYS
71b
Exploring Dark Matter and Dark Energy in the New Universe
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*Prerequisite: Familiarity with pre-calculus mathematics is required. Some knowledge of physics is recommended.*

Dark matter and dark energy make up 96 percent of the universe but we know very little about them. This course explores what we know and don't know, and what we hope to find out with new experiments and observations. Usally offered every second year.

John Wardle

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HSSP
100b
Introduction to Epidemiology, Biostatistics, and Population Health
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*Core course for the HSSP major and minor. Open to juniors and seniors only.*

Provides an orientation to the science of epidemiology, the quantitative foundation for public health policy. As a comprehensive survey course, students from varying academic backgrounds are introduced to biostatistics and major epidemiological concepts, and provided with training in their application to the study of health and disease in human populations. Case studies examine how environmental, physical, behavioral, psychological, and social factors contribute to the disease burden of populations. Usually offered every semester.

Staff

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LGLS
138b
Science on Trial
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Surveys the procedures and analytic methods by which scientific data enter into litigation and regulation/policy making. Introduces basic tools of risk analysis and legal rules of evidence. Case studies of tobacco litigation and regulation; use of DNA and other forensic evidence in the criminal justice system; the Woburn ground-water contamination case; and other topics to be selected, such as genetics in the courtroom, court-ordered Cesarean sections, polygraph testing, alternative medicine, and genetically modified foods. Usually offered every second year.

Daniel Breen

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LING
130a
Formal Semantics: Truth, Meaning, and Language
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*Prerequisite: LING 100a or permission of the instructor. LING 120b recommended.*

Explores the semantic structure of language in terms of the current linguistic theory of model-theoretic semantics. Topics include the nature of word meanings, categorization, compositionality, and plurals and mass terms. Usually offered every year.

Sophia Malamud

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LING
160b
Mathematical Methods in Linguistics
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An introduction to fundamental mathematical concepts needed for advanced work in linguistics and computational linguistics. Topics include: set theory, theory of relations, fundamentals of logic, formal systems, lambda calculus, formal language theory, theory of automata, basics of probability and statistics, game theory, and decision theory. Usually offered every year.

Sophia Malamud or Keith Plaster

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MATH
8a
Introduction to Probability and Statistics
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Discrete probability spaces, random variables, expectation, variance, approximation by the normal curve, sample mean and variance, and confidence intervals. Does not require calculus; only high school algebra and graphing of functions. Usually offered every semester.

Gail Peretti

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MATH
36a
Probability
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*Prerequisite: MATH 20a or 22b.*

Sample spaces and probability measures, elementary combinatorial examples. Conditional probability. Random variables, expectations, variance, distribution and density functions. Independence and correlation. Chebychev's inequality and the weak law of large numbers. Central limit theorem. Markov and Poisson processes. Usually offered every fall.

Staf

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MATH
36b
Mathematical Statistics
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*Prerequisite: MATH 36a or permission of the instructor.*

Probability distributions, estimators, hypothesis testing, data analysis. Theorems will be proved and applied to real data. Topics include maximum likelihood estimators, the information inequality, chi-square test, and analysis of variance. Usually offered every spring.

Mark Adler

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MATH
161a
Advanced Bifurcation Analysis in Dynamical Systems
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*Prerequisites: MATH 20a, MATH 23b, and MATH 37a.*

Exposes tools from modern theory of dynamical systems and bifurcations for general nonlinear differential equations (including infinite dimensional delayed or integral equations). Such systems are increasingly used in research or advanced models of natural and social phenomena. Usually offered every second year.

Jonathan Touboul

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PHSC
2b
Introductory Astronomy
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*Does not meet requirements for the major in physics.*

Elementary physical ideas will be used to discuss the life and death of stars, the structure of the galaxies, and the large-scale features and evolution of the universe. Usually offered every year.

Staff

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PHYS
10a
Introduction to Physical Laws and Phenomena I
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*Corequisite: MATH 10a or equivalent. Usually taken with PHYS 18a.*

An introduction to Newtonian mechanics, kinetic theory, and thermodynamics. Usually offered every year.

Staff

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PHYS
10b
Introduction to Physical Laws and Phenomena II
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*Prerequisite: PHYS 10a. Usually taken with PHYS 18b.*

An introduction to electricity and magnetism, optics, special theory of relativity, and the structure of the atom. Usually offered every year.

Staff

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PHYS
11a
Introductory Physics I
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*Corequisite: MATH 10b or the equivalent. Usually taken with PHYS 19a.*

An introduction to Newtonian mechanics with applications to several topics. Usually offered every year.

Staff

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PHYS
11b
Introductory Physics II
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*Corequisite: MATH 10b or the equivalent. Usually taken with PHYS 19b. Prerequisite: PHYS 11a or equivalent.*

An introduction to electricity and magnetism and the special theory of relativity. Usually offered every year.

Richard Fell

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PHYS
15a
Advanced Introductory Physics I
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*Corequisite: MATH 10a or b or the equivalent, or permission of instructor. Usually taken with PHYS 19a.*

An advanced version of PHYS 11a for students with advanced preparation in physics and mathematics. An introduction to Newtonian mechanics with special applications to several topics. Usually offered every year.

Gabriella Sciolla

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PHYS
15b
Advanced Introductory Physics II
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*Prerequisite: PHYS 15a or the equivalent and MATH 10a or b or equivalent, or permission of instructor. Usually taken with PHYS 19b.*

An advanced version of PHYS 11b for students with good preparation in physics and mathematics. An introduction to electricity and magnetism and the special theory of relativity for students with advanced preparation. Usually offered every year.

Marcelle Soares-Santos

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PHYS
39a
Advanced Physics Laboratory
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*Prerequisite: PHYS 20a. This course may be repeated once for credit with permission of the instructor. This course is co-taught with PHYS 169b.*

Experiments in a range of topics in physics, possibly including selections from the following: wave optics, light scattering, Nuclear Magnetic Resonance, numerical simulation and modeling, phase transitions, laser tweezers, chaotic dynamics, and optical microscopy. Students work in depth on three experiments during the term. Usually offered every year.

Seth Fraden

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POL
50b
Political Science Methods: Research, Design, and Modes of Analysis
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*Prerequisite: Sophomore standing or higher. May not be taken for credit by students who took POL 100b in prior years.*

An introduction to nonstatistical research methods for analyzing political processes. Moves from selecting problems to composing a focused research question, examining relevant theory, conceptualizing variables, generating hypotheses, research design, research operations, and analysis. Uses examples from comparative, international, and American politics. Usually offered every year.

Jill Greenlee

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POL
52a
Basic Statistics for Social and Political Analysis
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Provides a foundation in statistics focusing on descriptive statistics, inference, hypothesis testing and the basics of regression analysis. Becoming familiar with basic statistics will help you to prepare for a career as a social scientist. Usually offered every second year.

Alejandro Trelles

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POL
54a
Polling the American Public
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Workshop where students will learn to create, conduct, and analyze a national public opinion poll. Usually offered every year.

Amber Spry

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PSYC
51a
Statistics
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*Prerequisite: PSYC 10a (formerly PSYC 1a) or the permission of the instructor. This course normally should be completed by the end of the sophomore year. *

Covers the fundamentals of descriptive and inferential statistics. Techniques useful in the behavioral sciences will be emphasized. Students learn the theory of statistical decisions, practical application of statistical software, and how to analyze journal articles. Usually offered every semester.

Staff

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PSYC
51aj
Statistics
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*Prerequisite: PSYC 10a or the permission of the instructor.*

Covers the fundamentals of descriptive and inferential statistics. Techniques useful in the behavioral sciences will be emphasized. Students learn the theory of statistical decisions, practical application of statistical software, and how to analyze journal articles. Offered as part of JBS program.

Staff

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PSYC
52a
Research Methods and Laboratory in Psychology
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*Prerequisites: PSYC 10a (formerly PSYC 1a) and 51a. In order to pre-enroll in this course, students must consult with the department one semester before anticipated enrollment. This course normally should be completed by the end of the sophomore year. *

The laboratory/lecture offers supervised practice in experimental design, data analysis and interpretation, and formal presentation of experimental results. Usually offered every semester.

Ellen Wright and Staff

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PSYC
52aj
Research Methods and Laboratory in Psychology
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*Prerequisites: PSYC 10a. Corequisite: PSYC 51aj.*

The laboratory/lecture offers supervised practice in experimental design, data analysis and interpretation, and formal presentation of experimental results. Offered as part of JBS program.

Staff

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PSYC
140a
Statistical Analysis Software (SAS) Applications
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*Prerequisite: PSYC 51a. Some introductory statistics experience will be helpful but not required. No prior SAS experience is required. *

Designed for those who are interested in learning to use SAS. By using actual examples (data), students will have a hands-on experience using SAS for data management, data report, descriptive statistics, graphics, and some inferential statistics. Usually offered every year.

Xiaodong Liu

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PSYC
148a
Applied Statistical Computing in R
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*Prerequisite: PSYC 51a or equivalent.*

Designed for graduate students and advanced undergraduates who like to learn the R statistical programming package, further their understanding of statistical modeling and its application in applied and academic research, use R to make the connection between statistical concepts, modeling, and their implementation, and use R to document their research process and enhance its reproducibility. Usually offered every second year.

Xiaodong Liu

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SOC
182a
Applied Research Methods
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Provides an introduction to research methods and quantitative analysis commonly used in sociology. Using quantitative data, the class explores how higher education reflects the social stratification found in U.S. society. Participants will read peer-reviewed journal articles; design their own survey and analyze the results; and conduct analysis on a national data set focused on education. The course assumes no prior knowledge of research methods, but it does assume a curiosity about why we conduct research, how research studies are designed, and a willingness to analyze the results of different research studies. Usually offered every second year.

Staff