Why are people superstitious? Why do people blush when they are embarrassed? What is intelligence (and are IQ tests a good way to measure it)? Why don't psychopaths feel guilty when they harm others? How reliable are childhood memories? Why do we laugh? Do violent video games make people act violently? Why do some people seem instantly trustworthy and others seem creepy? How do we choose whom to sleep with, date, or marry? How does stress affect our body? While questions like these have been asked for centuries, psychology has begun to provide answers to these - and other questions about the human mind - by applying the tools of scientific investigation. In this course you will receive a broad introduction to the science of psychology: from the history of the field and its major advances, to the latest research on topics such as perception, memory, intelligence, morality, sexuality, mental illness, religion, language, and creativity. You will also learn about the tools and methods psychologists use to investigate the mind, such as observing how the mind of a child changes and develops over time, looking at people across cultures, measuring brain activity, and experimentally manipulating everything from the shape of a figure presented on a computer screen, to the smell of a room, or the attractiveness of the experimenter.

Full details for PSYCH 1101 - Introduction to Psychology

This course provides an introduction to the science of the mind. Everyone knows what it's like to think and perceive, but this subjective experience provides little insight into how minds emerge from physical entities like brains. To address this issue, cognitive science integrates work from at least five disciplines: Psychology, Neuroscience, Computer Science, Linguistics, and Philosophy. This course introduces students to the insights these disciplines offer into the workings of the mind by exploring visual perception, attention, memory, learning, problem solving, language, and consciousness.

Full details for PSYCH 1102 - Introduction to Cognitive Science

This section is highly recommended for students who are interested in learning about the topics covered in the main course through writing and discussion.

Full details for PSYCH 1104 - WIM: Introduction to Cognitive Science

Personality and Social Psychology area are interested in understanding how people think, feel, and act in real-world social situations. There is a particular interest in how people make sense of the social world around them, as represented by research programs on judgment and decision making, attribution, self-knowledge, affect and emotion, and stereotyping/prejudice. Frequent topics of inquiry include whether people reach accurate or erroneous judgments about themselves and others, how people arrive at their decisions, and how those decisions can be influenced by emotions or factors outside of awareness and more.

Full details for PSYCH 1120 - FWS:Personality & Social Psychology

Introduction to Human Development provides a broad and foundational overview of field of human development, starting from conception and ending through process of death and dying. The course will start with an outline and explanation of the lifespan perspective in human development. The biological beginnings of life and prenatal development will serve as the start of the discussion of human development, followed by an exploration of physical, cognitive, and socioemotional development at each subsequent stage within the lifespan (e.g., infancy, early childhood, middle & late childhood, etc.). Discussion of each developmental stage will highlight major research findings and their real-world application.

Full details for PSYCH 1131 - Introduction to Human Development

How do we perceive, learn about, and store information about the environments around us? How does what we have learned affect how we perceive and understand? PCD researchers in the graduate field of psychology at Cornell study human perception, language, and memory, as well as the development of various cognitive functions in infants. The methods they use are diverse, and range from human behavioral experiments in development, perception, and psycholinguistics, through computational modeling and simulation of auditory, visual, and language processes, to human electrophysiology by means of event-related potential (ERP) analysis.

Full details for PSYCH 1140 - FWS: Perception, Cognition, and Development

Environmental Psychology is an interdisciplinary field concerned with how the physical environment and human behavior interrelate. Most of the course focuses on how residential environments and urban and natural settings affect human health and well-being. Students also examine how human attitudes and behaviors affect environmental quality. Issues of environmental justice and culture are included throughout. Hands-on projects plus exams.

Full details for PSYCH 1500 - Introduction to Environmental Psychology

Human-Environment Relations is an interdisciplinary field concerned with how the physical environment and human behavior interrelate. Most of the course focuses on how residential environments and urban and natural settings affect human health and well-being. Students also examine how human attitudes and behaviors affect environmental quality. Issues of environmental justice and culture are included throughout. Hands-on projects plus exams. Lecture and discussion sections. WIM section attends a regular lecture but also meets weekly with a graduate writing instructor. The two principal objectives of WIM section:1. More in depth discussion and analysis of the materials covered in the course.2. On going, systematic opportunity to improve your writing and presentation skills.

Full details for PSYCH 1501 - Introduction to Environmental Psychology - Writing in the Major

The most significant problems that humans face - climate change, sectarian violence, political polarization, the spread of misinformation, etc. - are problems that we've made for ourselves. In this lecture course, we will probe the depths of human stupidity by exploring research on the nature of human reasoning, decision-making, beliefs, and more.

Full details for PSYCH 2100 - The Science of Human Stupidity

Introduction to psychology from a biological perspective, which focuses on brain mechanisms of behavior. Topics include the structure and function of the nervous system, physiological approaches to understanding behavior, hormones and behavior, biological bases of sensation and perception, learning and memory, cognition, emotion, and communication.

Full details for PSYCH 2230 - Intro to Behavioral Neuroscience

The Pursuit of Happiness is even mentioned in the Declaration of Independence, but what does this mean? This course will explore the kinds of happiness found in human experience, including financial success, public service, romantic and family life, political and cultural identity, as well as the power of music, literature, art and film to affect mood and self-awareness.

Full details for PSYCH 2450 - Pursuing Happiness

In a complex environment with many sources of variability, how can one tell with confidence whether a particular observed effect is real? And how much confidence is appropriate? This course introduces the principles of statistical description and inference as strategies to answer these questions, with emphasis on methods of principal relevance to psychology, neuroscience, and the behavioral sciences.

Full details for PSYCH 2500 - Statistics and Research Design

This course is modeled after Great Books literature courses in the humanities, but with two important differences: we read non-fiction books in the social sciences rather than the humanities, written by highly prominent contemporary social scientists. The course title refers to the fact that the books are new, hence their potential greatness has yet to be confirmed by the test of time. We choose living authors to give students a unique opportunity: to interact with each of the six authors in Q&A sessions via live or recorded video conferencing. Great Books courses are organized around books rather than the more traditional theme-based approach in most undergraduate classes, and each book is intended to stand on its own. Although the topics vary widely, each of the books addresses fundamental puzzles that motivate social science inquiry regarding human behavior and social interaction. These puzzles cut across disciplinary boundaries, hence the course is co-taught by psychologist Steve Ceci and sociologist/information scientist Michael Macy who provide continuity by calling attention to similarities and differences in theories, concepts, assumptions, and methods between sociologists (who focus on what happens between individuals) and psychologists (who focus on what happens within individuals). The authors vary from year to year but include famous social scientists such as Claude Steele, Daniel Kahneman, Nicholas Christakis, Beverly Tatum, Malcolm Gladwell, and Steven Pinker.

Full details for PSYCH 2580 - Six Pretty Good Books: Explorations in Social Science

What is personality? How is it scientifically studied and measured? To what extent, do biological, social, and cultural factors shape personality? Is personality an expression of our genetic make up and biology, the culmination of social influences, the interplay of both, or the result of random events? In this course, we will review the major theoretical paradigms of personality psychology, discuss contemporary research, theory, and methodology, and learn about key historical debates in the study of personality.

Full details for PSYCH 2750 - Introduction to Personality

This course will introduce students to the basics of research design and will review several methodologies in the study of human development. The focus of the course will be on descriptive and experimental methods. Students will learn the advantages and challenges to different methodological approaches. The course also places an emphasis on developing students' scientific writing and strengthening their understanding of statistics.

Full details for PSYCH 2830 - Research Methods in Human Development

Intro to Data Science for Social Scientists using R.

Full details for PSYCH 2930 - Introduction to Data Science for Social Scientists

Focuses on how the scientific study of human memory interfaces with the theory and practice of law.

Full details for PSYCH 3190 - Memory and the Law

This course is designed to provide an introduction to experimental research on the neural basis of behavior and cognition in animals. Topics will include basic neuroanatomy and neurophysiology, neural and hormonal control of behavior, and learning and memory. Students will gain extensive hands on experience with a variety of laboratory techniques, and animal species, and behaviors.

Full details for PSYCH 3240 - Behavioral Neuroscience Laboratory

A theoretical and empirical approach to the biological, psychological, and social (including cultural and historical) aspects of adult psychopathology. Readings range from Freud to topics in psychopharmacology. The major mental illnesses are covered, including schizophrenia as well as mood, anxiety, and personality disorders. Childhood disorders are not covered.

Full details for PSYCH 3250 - Adult Psychopathology

Full details for PSYCH 4210 - Native American Psychology

This course explores what is known, and what remains unknown, about the neural circuits that control social behavior, including parental behavior, sexual behavior, aggression, and vocalization. How do neural circuits control and coordinate distinct social behaviors? How are sex-typical social behaviors generated? How do past experiences and internal states influence social behavior, and what are the neural mechanisms for these effects? This course focuses mainly, although not exclusively, on research performed in non-human animals, and we'll also examine differences and similarities in the neural circuits for social behavior across species.

Full details for PSYCH 4390 - Neural Circuits for Social Behavior

New technologies are changing our world at a rapid pace. In many cases, the society does not fully understand the impact of technology and is not prepared for the speed of the change that is occurring. This course will explore a few of these new technologies and investigate their effects on the users and on the society at large. The topics that will be explored include face recognition, virtual reality, violence in media, general AI, and the technological singularity. We will look at the ways in which these technologies affect our lives, with a focus on education, entertainment, employment, politics, and the future of humanity.

Full details for PSYCH 4420 - The Psychology and Ethics of Technology

This course on the climate crisis acquaints students with the psychological factors underlying ecocide and anthropogenic climate change and the possible avenues for its mitigation, with a particular focus on climate justice and Indigenous knowledges and ways of relating to nature. In parallel with reading and discussing primary literature on these topics, students work on research projects, complementing theory with practice and placing it in the local geopolitical context.

Full details for PSYCH 4430 - Confronting Climate Change

This course will give an opportunity to learn how to communicate concepts and knowledge from the psychological sciences. We will examine the challenges associated with science communications, including ways to engage the perspectives of diverse audiences, and evaluation of the effects of the interaction on the audience's knowledge and attitudes. Most of our activities will focus on the development of exhibits for the Sciencenter of Ithaca. We will develop exhibit prototypes, evaluate the public's engagement and learning from them, and use the feedback to refine our prototypes. The goal will be to effectively convey current understanding of psychological processes to the general public, with an emphasis on engaging young children.

Full details for PSYCH 4500 - Psychology at the Sciencenter!

Full details for PSYCH 4510 - Research Seminar on the Relational Mind

Each year, more than 100 million people worldwide develop clinically recognizable depression. Because of its prevalence, depression is sometimes called the common cold of psychopathology. This course provides a wide-ranging examination of the theories, methods, and major controversies in mood disorders research, including coverage of social, cognitive, and biological perspectives.

Full details for PSYCH 4670 - Advanced Seminar in Mood Disorders

Practice in planning, conducting, and reporting independent laboratory, field, and/or library research.

Full details for PSYCH 4700 - Undergraduate Research in Psychology

Advanced experience in planning, conducting, and reporting independent laboratory, field, and/or library research. One, and preferably two, semesters of PSYCH 4700 is required. The research should be more independent and/or involve more demanding technical skills than that carried out in PSYCH 4700.

Full details for PSYCH 4710 - Advanced Undergraduate Research in Psychology

Full details for PSYCH 4770 - Advanced Developmental Seminar

The focus of this course is on discussion and critical analysis of selected articles from very recent issues of the most selective social psychological journals. Readings are chosen for their importance, their coverage of contemporary topics in social psychology, and their potential for generating stimulating discussion . Students write brief thought papers before each class in which they offer suggestions for class discussion based on their close reading of the day's assigned articles. They also write a term paper (details at first class meeting).

Full details for PSYCH 4810 - Advanced Social Psychology

This course is designed to introduce first-year graduates to the Psychology Department faculty through a weekly series of presentations of current research.

Full details for PSYCH 6000 - General Research Seminar

This course enhances the graduate experience and prepares first-year psychology graduate students for success. The student receives a formal introduction to conceptualizing and articulating a research project, science writing, the grant proposal and review processes, and numerous other aspects of professional development. The course serves as an opportunity for preparation for graduate studies and a career in academics or a related profession.

Full details for PSYCH 6001 - Graduate Professionalism Seminar

This course will cover special topics related to belief, metacognition, and reasoning.

Full details for PSYCH 6225 - Special Topics in Social Psychology

This course is offered to graduate students and focuses on discussion of topics in quantitative methods, with an emphasis on current books. Each semester students will work through a contemporary advanced monograph on methods. We will be using social annotation software to prepare for readings and then have class discussion of chapters. There will be a special emphasis on causal inference and foundational research methods.

Full details for PSYCH 6226 - Special Topics in Quantitative Psychology

Course explores current issues in Psychology. Topics vary by section.

Full details for PSYCH 6271 - Topics in Biopsychology

Full details for PSYCH 6500 - Psychology at the Sciencenter!

Full details for PSYCH 6510 - Research Seminar on the Relational Mind

Full details for PSYCH 6770 - Advanced Developmental Seminar

The focus of this course is on discussion and critical analysis of selected articles from very recent issues of the most selective social psychological journals. Readings are chosen for their importance, their coverage of contemporary topics in social psychology, and their potential for generating stimulating discussion. Students write brief thought papers before each class in which they offer suggestions for class discussion based on their close reading of the day's assigned articles. They also write a term paper on a social psychological topic of their own choosing.

Full details for PSYCH 6810 - Advanced Social Psychology

A graduate research seminar in biopsychology.

Full details for PSYCH 7000 - Research in Biopsychology

A graduate research seminar in human experimental psychology.

Full details for PSYCH 7100 - Research in Human Experimental Psychology

A graduate research seminar in social psychology and personality.

Full details for PSYCH 7200 - Research in Social Psychology and Personality

First semester of a year-long discussion-seminar course intended to give graduate students an in-depth understanding of current research and theory in social psychology. Emphasizes social cognition, but other topics, such as group dynamics, social influence, moral psychology, and emotional experience, are covered.

Full details for PSYCH 7750 - Proseminar in Social Psychology I

A graduate seminar on doctoral thesis research in biopsychology.

Full details for PSYCH 9000 - Doctoral Thesis Research in Biopsychology

A graduate seminar on doctoral thesis research in human experimental psychology.

Full details for PSYCH 9100 - Doctoral Thesis Research in Human Experimental Psychology

A graduate seminar on doctoral thesis research in social psychology and personality.

Full details for PSYCH 9200 - Doctoral Thesis Research in Social Psychology and Personality

CHEM 1007 reviews material presented in CHEM 2070 lectures and also provides problem-solving strategies and practice during the discussion sections.

Full details for CHEM 1007 - Academic Support for CHEM 2070

Reviews material presented in CHEM 3570 lectures and offers practice with CHEM 3570 material. Weekly reviews and problem solving sessions focus on the most important topics covered in lecture, and office hours held throughout the week by Learning Strategies Center tutors to help improve performance in CHEM 3570.

Full details for CHEM 1057 - Academic Support for CHEM 3570

Fundamentals of chemistry will be introduced and applied to real world situations. Critical aspects of 21st century life depend on an informed voting public that can assiduously address scientific issues. The role of chemistry, the good and the bad, will be an increasingly important component of everyday life. The course seeks to prepare you to be an informed voter.

Full details for CHEM 1150 - The Language of Chemistry

CHEM 1560 is the lecture component of a one-semester introduction to fundamental topics in general chemistry, both qualitative and quantitative. Co-enrollment in CHEM 1561 (lab) is required. CHEM 1560 (lecture) and CHEM 1561 (lab) together provide a complete one-semester introduction to general chemistry and serve as preparation for CHEM 1570. CHEM 1560 is not recommended for premedical or pre-veterinary students. Students planning to take CHEM 2080 should be enrolled in CHEM 2070 rather than CHEM 1560.

Full details for CHEM 1560 - Introduction to General Chemistry

CHEM 1561 is the laboratory component of a one-semester introduction to fundamental topics in general chemistry, both qualitative and quantitative. Co-enrollment in CHEM 1560 (lecture) is required. CHEM 1560 (lecture) and CHEM 1561 (lab) together provide a complete one-semester introduction to general chemistry and serve as preparation for CHEM 1570. CHEM 1560 and CHEM 1561 are not recommended for premedical or pre-veterinary students. Students planning to take CHEM 2080 and CHEM 2081 should be enrolled in CHEM 2070 and CHEM 2071 rather than CHEM 1560 and CHEM 1561.

Full details for CHEM 1561 - Introduction to General Chemistry Laboratory

Solve It! will teach the skill of solving cognitively challenging general chemistry questions, such as students receive in CHEM 2070. Students will explore Polya's method of problem solving while solving problems on unit conversions, combustion analysis, limiting reactants, isotopes, the Bohr model, periodic trends, 3-D Lewis structures, atomic orbitals, molecular orbitals, ideal gases, and the kinetic theory of gases. In addition, students will learn fundametal arithmetic and mathematical skills.

Full details for CHEM 1729 - Solve It!

CHEM 2070 is the lecture component of General Chemistry I. Covers fundamental chemical principles, with considerable attention given to the quantitative aspects and techniques important for further work in chemistry. Main topics include chemical transformations and equations, periodic trends of the elements, electronic structure of atoms, chemical bonding, and the collective behavior of molecules.

Full details for CHEM 2070 - General Chemistry I

This is the laboratory component of CHEM 2070 General Chemistry I. Covers fundamental chemical principles, with considerable attention given to the quantitative aspects and techniques important for further work in chemistry. Main topics include chemical transformations and equations, periodic trends of the elements, electronic structure of atoms, chemical bonding, and the collective behavior of molecules.

Full details for CHEM 2071 - General Chemistry I Laboratory

CHEM 2080 is the lecture component of General Chemistry II. Covers fundamental chemical principles, including reaction kinetics, thermodynamics, and equilibrium. These principles are presented quantitatively and explored in the laboratory. Considerable attention is given to the quantitative calculations and techniques important for further work in chemistry.

Full details for CHEM 2080 - General Chemistry II

CHEM 2081 is the laboratory component of General Chemistry II. Covers fundamental chemical principles, including reaction kinetics, thermodynamics, and equilibrium. These principles are presented quantitatively and explored in the laboratory. Considerable attention is given to the quantitative calculations and techniques important for further work in chemistry.

Full details for CHEM 2081 - General Chemistry II Laboratory

CHEM 2090 is the lecture component of Engineering General Chemistry. Covers basic chemical concepts, such as reactivity and bonding of molecules, introductory quantum mechanics, and intermolecular forces in liquids and solids and gases. Attention will be focused on aspects and applications of chemistry most pertinent to engineering.

Full details for CHEM 2090 - Engineering General Chemistry

CHEM 2091 is the laboratory component of CHEM 2090 Engineering General Chemistry. Covers basic chemical concepts, such as reactivity and bonding of molecules, introductory quantum mechanics, and intermolecular forces in liquids and solids and gases. Attention will be focused on aspects and applications of chemistry most pertinent to engineering.

Full details for CHEM 2091 - Engineering General Chemistry Laboratory

Intensive systematic study of the laws and concepts of chemistry, with considerable emphasis on quantitative aspects. CHEM 2150 covers electronic structure of atoms, chemical bonding, thermodynamics, kinetics, and equilibrium. This course serves as an accelerated entry into organic chemistry in the Spring semester for students with a strong background in chemistry. Laboratory work covers qualitative and quantitative analysis, thermodynamics, kinetics transition metal chemistry, and spectroscopic techniques.

Full details for CHEM 2150 - Honors General and Inorganic Chemistry

Introduction to the synthesis, separation, characterization, and handling of materials, including chromatography, extraction, crystallization, infrared spectroscopy, and others. An experiment is performed the first week of lab. Students need to enroll in the course Canvas site and complete the appropriate pre-lab assignments outlined on that site before coming to the first lab.

Full details for CHEM 2510 - Introduction to Experimental Organic Chemistry

CHEM 2770 is the first teaching methods companion class to CHEM 2070 and CHEM 2080. CHEM 2770 students will co-lead weekly 2-hour review sessions; meet in 2-hour group meetings to develop and refine teaching materials; attend a 1-hour discussion class on a current STEM pedagogical theory; and assess teaching progress for 1-hour (all activities on a weekly basis).

Full details for CHEM 2770 - Methods in Chemical Education I

CHEM 2780 is the second teaching methods companion class to CHEM 2070 and CHEM 2080. CHEM 2780 students will co-lead weekly 2-hour review sessions; meet in 2-hour group meetings to develop and refine teaching materials; attend a 1-hour discussion class on a current STEM pedagogical theory; and assess teaching progress for 1-hour (all activities on a weekly basis).

Full details for CHEM 2780 - Methods in Chemical Education II

Chemical and instrumental methods of analysis, including fluorescence spectroscopy, electrochemistry, UV-vis absorption spectroscopy, infrared spectroscopy, and gas chromatography. Error analysis, experiment design, and data analysis using Jupyter notebooks.

Full details for CHEM 3020 - Honors Experimental Chemistry II

Study of the important classes of carbon compounds-including those encountered in the biological sciences. The course emphasizes their three-dimensional structures, mechanisms of their characteristic reactions, their synthesis, methods of identifying them, and their role in modern science and technology.

Full details for CHEM 3570 - Organic Chemistry for the Life Sciences

The course emphasizes the important classes of organic compounds, with particular emphasis on their three-dimensional structures, mechanisms of their characteristic reactions, their synthesis, methods for their identification, and their applications in modern technology and medicine.

Full details for CHEM 3580 - Organic Chemistry for the Life Sciences

Rigorous and systematic study of organic chemistry with a focus on molecules that have biological applications. The course emphasizes a mechanistic understanding of organic reactions and applies this knowledge toward complex systems such as amino acids and carbohydrates.

Full details for CHEM 3600 - Honors Organic Chemistry II

Survey of the fundamental principles of physical chemistry, The course covers thermodynamics, chemical kinetics, enzyme kinetics, and the electronic structure of atoms and molecules. CHEM 3870 satisfies the minimum requirement for physical chemistry for the chemistry major.

Full details for CHEM 3870 - Principles of Physical Chemistry

CHEM 3890-CHEM 3900 is a year-long sequence covering key topics in physical chemistry. CHEM 3890 introduces the use of mathematics and physics to investigate chemical systems. The fundamental principles of quantum mechanics are introduced and applied to understanding the structure and spectra of atoms and molecules. Specific topics include exact and approximate solutions to the Schrodinger equation, angular momentum, bonding and molecules, and spectroscopy. CHEM 3900 follows with an introduction to the behavior of ensembles of quantum particles (statistical mechanics), the laws of thermodynamics, and kinetic theory.

Full details for CHEM 3890 - Honors Physical Chemistry I

Research in inorganic chemistry involving both laboratory and library work, planned in consultation with a faculty member.

Full details for CHEM 4210 - Introduction to Inorganic Chemistry Research

Research in analytical chemistry involving both laboratory and library work, planned in consultation with a faculty member.

Full details for CHEM 4330 - Introduction to Analytical Chemistry Research

Research in chemical biology involving both laboratory and library work, planned in consultation with a faculty member.

Full details for CHEM 4430 - Introduction to Chemical Biology Research

This course provides an introduction to both the fundamental biochemistry of living systems, including the structure and synthesis of biological macromolecules, and modern approaches that combine organic chemistry with emerging techniques from the chemical and life sciences to interrogate biological systems.

Full details for CHEM 4500 - Principles of Chemical Biology

Research in organic chemistry involving both laboratory and library work, planned in consultation with a faculty member.

Full details for CHEM 4610 - Introduction to Organic Chemistry Research

Research in physical chemistry involving both laboratory and library work, planned in consultation with a faculty member.

Full details for CHEM 4770 - Introduction to Physical Chemistry Research

Discussion of and demonstration of facilities relevant to modern chemical research.

Full details for CHEM 5110 - Chemical Facilities Boot Camp

Supervision of Capstone Research Project.

Full details for CHEM 5120 - Capstone Research Project

A group theoretical analysis of bonding in main group compounds will be followed by a survey of modern coordination chemistry, including rudimentary spectroscopy and magnetism, and inorganic reaction mechanisms.

Full details for CHEM 6050 - Advanced Inorganic Chemistry I: Symmetry, Structure, and Reactivity

Electrochemistry is involved with electrified interfaces and the interaction/interconversion of chemical and electrical energy. This course focuses on the fundamentals of interfacial phenomena including electrode kinetics, electron transfer theory, the electrical double layer, mass transport, and diffusion processes. The course will cover a broad range of electrochemical methods to advance our understanding of structure-property relationships of energy materials. The course will also include selected current topics including: (1) Advanced renewable energy conversion and storage technologies, such as CO2 reduction, H2 production, lithium batteries, and solar cells. (2) Introduction to the state-of-the-art development of analytical methods including electron microscopy and X-ray methods. (3) Electrochemistry with interdisciplinary overlap with solid-state chemistry and materials science, such as photoelectrochemistry, organic electrochemistry, and bioelectrochemistry.

Full details for CHEM 6291 - Electrochemistry of Energy Materials

This course provides an introduction to both the fundamental biochemistry of living systems, including the structure and synthesis of biological macromolecules, and modern approaches that combine organic chemistry with emerging techniques from the chemical and life sciences to interrogate biological systems.

Full details for CHEM 6450 - Principles of Chemical Biology

The course focuses on stereoelectronic properties of organic compounds, conformational analysis, reaction thermodynamics and kinetics, stereochemistry, reactive intermediates, and catalysis. Case studies will focus on applications of these concepts and corresponding techniques that lead to creative design of selective organic synthesis and mechanistic insights into complex organic transformations. A particular emphasis is on the development of chemical and mechanistic intuition that will facilitate the students' laboratory research efforts.

Full details for CHEM 6650 - Advanced Organic Chemistry

Catalysis is fundamental and essential to modern organic synthesis. This course will cover topics in transition metal catalysis, biocatalysis, photoredox catalysis, and electrosynthesis with a focus on reaction mechanism and synthetic applications. Topics of current interest are emphasized. Transition metal-based catalysts are invaluable in both organic and polymer synthesis. This course begins with an overview of organometallic chemistry and catalysis. Subsequent modules on catalytic synthesis of small molecules and polymers are then presented. Topics of current interest are emphasized.

Full details for CHEM 6690 - Modern Catalytic Reactions in Organic Synthesis

Physical studies of proteins, with emphasis on using single molecule methodologies and on studies of metalloproteins. Topics include: Physical/chemical concepts that include chemical structure and conformation of proteins, protein folding energy landscape, electron transfer theory, enzyme catalysis, chemical kinetics, and single-molecule kinetics. Experimental methodologies that include absorption and emission spectroscopy, fluorescence energy resonance transfer, confocal microscopy, total internal reflection fluorescence, single molecule spectroscopy, time correlated single photon counting, fluorescence correlation spectroscopy, atomic force microscopy, optical tweezers, magnetic tweezers, super-resolution imaging with optical microscopy. Protein structure and function that includes metalloprotein structure/function (bioinorganic chemistry), GFP and variants, protein labeling, motor proteins, protein-protein interactions, protein-DNA interactions, and live-cell imaging.

Full details for CHEM 6860 - Physical Chemistry of Proteins

CHEM 6890-CHEM 6900 is a year-long sequence covering key topics in physical chemistry. CHEM 6890 introduces the use of mathematics and physics to investigate chemical systems. The fundamental principles of quantum mechanics are introduced and applied to understanding the structure and spectra of atoms and molecules. Specific topics include exact and approximate solutions to the Schrodinger equation, angular momentum, bonding and molecules, and spectroscopy.

Full details for CHEM 6890 - Honors Physical Chemistry I

The chief aim of this course is to provide an understanding of how the tools of modern spectroscopy can be applied to unravel the structural and dynamical properties of molecular systems, with a focus on optical techniques. The course will briefly cover the theoretical basis of light-matter interactions and factors governing the vibrational and electronic spectra of diatomic and polyatomic molecules. The main portion of the course will address current topics in spectroscopic research with a survey of different techniques and the theory behind them. By the end of the course, students will be equipped to understand and interpret the results of a wide array of steady-state and optical spectroscopic techniques applied to complex molecules.

Full details for CHEM 7910 - Advanced Spectroscopy

A modern introduction to quantum mechanics (QM). Topics will include: the quantum state vector, the probabilistic interpretation of QM, the mathematical language of QM, angular momentum, QM in the continuum, solutions to the Schrodinger equation for simple 1D applications, the coulomb potential and the hydrogen-atom, independent particles, the variational approach, and time-independent perturbation theory.

Full details for CHEM 7930 - Quantum Mechanics I

Introduces the fundamentals of statistical mechanics: ensembles, distributions, averages, and fluctuations, building to the treatment of systems of interacting molecules. Topics from equilibrium statistical mechanics include structure and thermodynamics of molecular liquids, critical phenomena, and computational statistical mechanics. Topics from nonequilibrium statistical mechanics include spectroscopy, chemical kinetics, transport, and the microscopic origins of irreversibility.

Full details for CHEM 7960 - Statistical Mechanics

Reviews material presented in MATH 1106 lectures and provides further instruction for students who need reinforcement, including problem-solving techniques and tips as well as prelim review. Not a substitute for attending MATH 1106 lectures or discussions. Students should contact their college for the most up-to-date information regarding if and how credits for this course will count toward graduation, and/or be considered regarding academic standing.

Full details for MATH 1006 - Academic Support for MATH 1106

Reviews material presented in MATH 1110 lectures and provides further instruction for students who need reinforcement, including problem-solving techniques and tips as well as prelim review. Not a substitute for attending MATH 1110 lectures or discussions. Students should contact their college for the most up-to-date information regarding if and how credits for this course will count toward graduation, and/or be considered regarding academic standing.

Full details for MATH 1011 - Academic Support for MATH 1110

Introduces topics in calculus: limits, rates of change, definition of and techniques for finding derivatives, relative and absolute extrema, and applications. The calculus content of the course is similar to 1/3 of the content covered in MATH 1106 and MATH 1110. In addition, the course includes a variety of topics of algebra, with emphasis on the development of linear, power, exponential, logarithmic, and trigonometric functions. Because of the strong emphasis on graphing, students will have a better understanding of asymptotic behavior of these functions.

Full details for MATH 1101 - Calculus Preparation

The goal of this course is to give students a strong basis in quantitative skills needed in the life and social sciences. We will focus on modeling using fundamental concepts from calculus developed in the course, including derivatives, integrals, and introductory differential equations. Examples from the life sciences are used throughout the course, including predator-prey populations. We will discuss mathematical models describing the evolution of these populations, analyze quantitative and qualitative properties to make predictions about these populations, and discuss assumptions and limitations of these models. Derivatives and integrals will be covered with a more applied focus than in MATH 1110 or a typical high school calculus course. Students who plan to take more than one semester of calculus should take MATH 1110 rather than MATH 1106.

Full details for MATH 1106 - Modeling with Calculus for the Life Sciences

MATH 1110 can serve as a one-semester introduction to calculus or as part of a two-semester sequence in which it is followed by MATH 1120. Topics include functions and graphs, limits and continuity, differentiation and integration of algebraic, trigonometric, inverse trig, logarithmic, and exponential functions; applications of differentiation, including graphing, max-min problems, tangent line approximation, implicit differentiation, and applications to the sciences; the mean value theorem; and antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, and the area under a curve.

Full details for MATH 1110 - Calculus I

Focuses on integration: applications, including volumes and arc length; techniques of integration, approximate integration with error estimates, improper integrals, differential equations and their applications. Also covers infinite sequences and series: definition and tests for convergence, power series, Taylor series with remainder, and parametric equations.

Full details for MATH 1120 - Calculus II

For students who wish to experience how mathematical ideas naturally evolve. The course emphasizes ideas and imagination rather than techniques and calculations. Homework involves students in actively investigating mathematical ideas. Topics vary depending on the instructor. Some assessment through writing assignments.

Full details for MATH 1300 - Mathematical Explorations

Introductory statistics course discussing techniques for analyzing data occurring in the real world and the mathematical and philosophical justification for these techniques. Topics include population and sample distributions, central limit theorem, statistical theories of point estimation, confidence intervals, testing hypotheses, the linear model, and the least squares estimator. The course concludes with a discussion of tests and estimates for regression and analysis of variance (if time permits). The computer is used to demonstrate some aspects of the theory, such as sampling distributions and the Central Limit Theorem. In the lab portion of the course, students learn and use computer-based methods for implementing the statistical methodology presented in the lectures.

Full details for MATH 1710 - Statistical Theory and Application in the Real World

How can you use writing to solve mathematical problems? Or even to discover problems that are worth solving? This course revisits high school mathematics with the goal of learning how mathematicians think about math. We will use writing to probe familiar math problems as well as discover new ones, and we will refine our ability to communicate their solutions. Readings will include excerpts from Lang’s Basic Mathematics and works by Gelfand. (These are high school math textbooks written by mathematicians with research careers.) The class will culminate in a research project: you will use writing to develop, investigate, and present your progress on a problem.

Full details for MATH 1890 - FWS: Writing in Mathematics

Essentially a second course in calculus and the first in a sequence designed for engineers that assumes familiarity with differential calculus at the level of MATH 1110. Topics include techniques of integration, finding areas and volumes by integration, exponential growth, partial fractions, infinite sequences and series, tests of convergence, and power series.

Full details for MATH 1910 - Calculus for Engineers

Introduction to multivariable calculus. Topics include partial derivatives, double and triple integrals, line and surface integrals, vector fields, Green's theorem, Stokes' theorem, and the divergence theorem.

Full details for MATH 1920 - Multivariable Calculus for Engineers

An introduction to linear algebra for students who plan to major or minor in mathematics or a related field. Topics include vector algebra, linear transformations, matrices, determinants, orthogonality, eigenvalues, and eigenvectors. Applications are made to linear differential or difference equations. Lectures will introduce students to formal proofs, and students will be required to produce some proofs in their homework and on exams. For a more applied version of this course, see MATH 2310.

Full details for MATH 2210 - Linear Algebra

An introduction to multivariable calculus for students who plan to major or minor in mathematics or a related field. Topics include differential and integral calculus of functions in several variables, line and surface integrals as well as the theorems of Green, Stokes and Gauss.

Full details for MATH 2220 - Multivariable Calculus

Designed for students who have been extremely successful in their previous calculus courses and for whom the notion of solving very hard problems and writing careful proofs is highly appealing, MATH 2230-MATH 2240 provides an integrated treatment of linear algebra and multivariable calculus at a higher theoretical level than in MATH 2210-MATH 2220. Topics covered in MATH 2230 include vectors, matrices, and linear transformations; differential calculus of functions of several variables; inverse and implicit function theorems; quadratic forms, extrema, and manifolds; multiple and iterated integrals.

Full details for MATH 2230 - Theoretical Linear Algebra and Calculus

An introduction to linear algebra for students interested in applications to data science. The course diverges from traditional linear algebra courses by emphasizing data science applications while teaching similar concepts. Key topics include matrices as data tables, high-dimensional datasets, singular value decomposition for data compression, and linear transformations in computer graphics. Students who take MATH 2310 may need more foundational coursework before pursuing further study in mathematics.

Full details for MATH 2310 - Linear Algebra for Data Science

An introduction to ordinary and partial differential equations. Topics include first-order equations (separable, linear, homogeneous, exact); mathematical modeling (e.g., population growth, terminal velocity); qualitative methods (slope fields, phase plots, equilibria and stability); numerical methods; second-order equations (method of undetermined coefficients, application to oscillations and resonance, boundary-value problems and eigenvalues); and Fourier series. A substantial part of this course involves partial differential equations, such as the heat equation, the wave equation, and Laplace's equation. MATH 2930 and MATH 2940 are independent and can be taken in either order; they should not be taken in the same semester.

Full details for MATH 2930 - Differential Equations for Engineers

Linear algebra and its applications. Topics include matrices, determinants, vector spaces, eigenvalues and eigenvectors, orthogonality and inner product spaces. Applications include brief introductions to difference equations, Markov chains, and systems of linear ordinary differential equations. May include computer use in solving problems. MATH 2930 and MATH 2940 are independent and can be taken in either order; they should not be taken in the same semester.

Full details for MATH 2940 - Linear Algebra for Engineers

A useful course for students who wish to improve their skills in mathematical proof and exposition, or who intend to study more advanced topics in mathematics. The methodology of proof provides a central tool for confirming the validity of mathematical assertions, functioning much as the experimental method does in the physical sciences. We will study various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and in set theory and combinatorics, then moving to applications and illustrations of these via topics in one or more of the three main pillars of mathematics: algebra, analysis, and geometry. Because cogent communication of mathematical ideas is important in the presentation of proofs, the course emphasizes clear, concise exposition.

Full details for MATH 3040 - Prove It!

Provides a transition from calculus to real analysis. Topics include rigorous treatment of fundamental concepts in calculus: including limits and convergence of sequences and series, compact sets; continuity, uniform continuity and differentiability of functions. Emphasis is placed upon understanding and constructing mathematical proofs.

Full details for MATH 3110 - Introduction to Analysis

A manifold is a type of subset of Euclidean space that has a well-defined tangent space at every point. Such a set is amenable to the methods of multivariable calculus. After reviewing some relevant calculus, this course investigates manifolds and the structures they are endowed with, such as tangent vectors, boundaries, orientations, and differential forms. The notion of a differential form encompasses such ideas as area forms and volume forms, the work exerted by a force, the flow of a fluid, and the curvature of a surface, space or hyperspace. We re-examine the integral theorems of vector calculus (Green, Gauss, and Stokes) in the light of differential forms and apply them to problems in partial differential equations, topology, fluid mechanics, and electromagnetism.

Full details for MATH 3210 - Manifolds and Differential Forms

A one-semester introduction to the theory and techniques of ordinary differential equations. Topics may include first-order and second-order differential equations, systems of linear differential equations, initial-value and two-point boundary-value problems, Sturm-Liouville theory, Sturm oscillation and comparison theory, the basic existence and uniqueness theorems, series solutions, special functions, and Laplace transforms. Applications from science and engineering may be included at the instructor’s discretion.

Full details for MATH 3270 - Introduction to Ordinary Differential Equations

An introductory course on number theory, the branch of algebra that studies the deeper properties of integers and their generalizations. Usually includes most of the following topics: the Euclidean algorithm, continued fractions, Pythagorean triples, Diophantine equations such as Pell's equation, congruences, quadratic reciprocity, binary quadratic forms, Gaussian integers, and factorization in quadratic number fields. May include a brief introduction to Fermat's Last Theorem.

Full details for MATH 3320 - Introduction to Number Theory

Basic problem-solving techniques and strategies for contest problems. Contest problems differ from standard mathematical instruction in that they are "contextless": the problem does not tell you which field it is in and sometimes goes to great lengths to disguise it. Understanding how to solve contest problems has applications to research, where knowing how to work with unknown concepts, how to attack a problem fluidly from the perspective of multiple fields, and different tricks for simplifying problems is extremely useful. This course will cover topics that appear in standard competitions (e.g., the Putnam exam), including combinatorics, number theory, geometry, and calculus. It will also teach strategies for understanding and attacking problems, more advanced proof techniques, and effective proof writing.

Full details for MATH 4040 - Patterns, Proofs, and Problems

Introduction to the rigorous theory underlying calculus, covering the real number system and functions of one variable. Topics typically include construction of the real number system, properties of the real number system, continuous functions, differential and integral calculus of functions of one variable, sequences and series of functions. Based entirely on proofs. The student is expected to know how to read and, to some extent, construct proofs before taking this course. More experience with proofs may be gained by first taking a 3000-level MATH course.

Full details for MATH 4130 - Honors Introduction to Analysis I

Covers complex variables, Fourier transforms, Laplace transforms and applications to partial differential equations. Additional topics may include an introduction to generalized functions. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course. Undergraduates who plan to attend graduate school in mathematics should take MATH 4180 rather than MATH 4220.

Full details for MATH 4220 - Applied Complex Analysis

Introduction to the fundamentals of numerical analysis: error analysis, approximation, interpolation, and numerical integration. In the second half of the course, we use these to build approximate solvers for ordinary and partial differential equations. Strong emphasis is placed on understanding the advantages, disadvantages, and limits of applicability for all the covered techniques. Computer programming is used to test the theoretical concepts throughout the course. Students will be expected to be comfortable writing proofs and have knowledge of programming. MATH 4250/CS 4210 and MATH 4260/CS 4220 can be taken independently from each other and in either order. Together they provide a comprehensive introduction to numerical analysis.

Full details for MATH 4250 - Numerical Analysis and Differential Equations

Introduction to linear algebra, including the study of vector spaces, linear transformations, matrices, and systems of linear equations. Additional topics include quadratic forms and inner product spaces, canonical forms for various classes of matrices and linear transformations. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course. Undergraduates who plan to attend graduate school in mathematics should take MATH 4330 instead of MATH 4310.

Full details for MATH 4310 - Linear Algebra

Honors version of a course in advanced linear algebra, which treats the subject from an abstract and axiomatic viewpoint. Topics include vector spaces, linear transformations, polynomials, determinants, tensor and wedge products, canonical forms, inner product spaces, and bilinear forms. Emphasis is on understanding the theory of linear algebra; homework and exams include at least as many proofs as computational problems. Strong proficiency in writing proofs is expected. More experience with proofs may be gained by first taking a 3000-level MATH course. MATH 4330-MATH 4340 is recommended for undergraduates who plan to attend graduate school in mathematics. For a less theoretical course that covers approximately the same subject matter as MATH 4330, see MATH 4310.

Full details for MATH 4330 - Honors Linear Algebra

Introduction to algebraic geometry and computational algebra. Students will learn how to compute a Gröbner basis for polynomials in many variables. Covers the following applications: solving systems of polynomial equations in many variables, solving diophantine equations in many variables, 3-colorable graphs, and integer programming. Such applications arise, for example, in computer science, engineering, economics, and physics. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.

Full details for MATH 4370 - Computational Algebra

Combinatorics studies discrete structures arising in mathematics, computer science, and many areas of application. Key topics include counting objects with specific properties (e.g., trees) and proving the existence of structures (e.g., matchings of all vertices in a graph). We cover basic questions in graph theory, including extremal graph theory (how large a graph must be to have a certain subgraph) and Ramsey theory (large objects are forced to have structure). An introduction to network flow theory and variations on matching theory, including theorems of Dilworth, Hall, König, and Birkhoff, are discussed. Methods of enumeration (inclusion/exclusion, Möbius inversion, and generating functions) are applied to problems of counting permutations, partitions, and triangulations. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.

Full details for MATH 4410 - Introduction to Combinatorics I

An introduction to projective, hyperbolic, and spherical geometry and their modern applications. The course will be divided into short modules with an emphasis on participation, discovery, and student projects and presentations. In addition to proving theorems, students will have the opportunity to make, build, 3D print, or program something related to the course material as a project component. We will cover classical theorems and techniques (e.g., stereographic projection and conics) and see how classical geometry is used in and relates to other areas of mathematics (e.g., topology, via Euler characteristic) and applications such as computer vision, networks, or architectural drawing. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.

Full details for MATH 4520 - Classical Geometries and Modern Applications

Topology may be described briefly as qualitative geometry. This course begins with basic point-set topology, including connectedness, compactness, and metric spaces. Later topics may include the classification of surfaces (such as the Klein bottle and Möbius band), elementary knot theory, or the fundamental group and covering spaces. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.

Full details for MATH 4530 - Introduction to Topology

An introduction to probability theory that prepares the student to take MATH 4720. The course begins with basics: combinatorial probability, mean and variance, independence, conditional probability, and Bayes formula. Density and distribution functions and their properties are introduced. The law of large numbers and central limit theorem are stated and their implications for statistics are discussed.

Full details for MATH 4710 - Basic Probability

An independent research course by arrangement with an individual professor. The goal is for the student to perform an independent investigation into a specific mathematical question. The student and professor will set expectations and grading policies at the beginning of the term.

Full details for MATH 4900 - Supervised Research

An independent reading course by arrangement with an individual professor. The goal is for the student to master a body of mathematics outside the normal curriculum. The student and professor will set expectations and grading policies at the beginning of the term.

Full details for MATH 4901 - Supervised Reading

Examines principles underlying the content of the secondary school mathematics curriculum, including connections with the history of mathematics, technology, and mathematics education research. One credit is awarded for attending two Saturday workshops (see e.math.cornell.edu/classes/math5080) and writing a paper. Other credit options are available for students completing additional work, such as tutoring at a local middle school or completing a research paper or project. Does not count toward the math major or math minor and will not count as degree credits for A&S students.

Full details for MATH 4980 - Special Study for Mathematics Teaching

This independent study course offers math majors (i.e., undergraduates whose applications to affiliate with the math major have been approved) an opportunity to reflect on concepts from mathematics as they were encountered and applied in a recent internship. Students write a short paper describing their work experience and how it connects to the educational objectives of the mathematics major.

Full details for MATH 4997 - Practical Training in Mathematics

Examines principles underlying the content of the secondary school mathematics curriculum, including connections with the history of mathematics, technology, and mathematics education research.

Full details for MATH 5080 - Special Study for Teachers

Covers complex variables, Fourier transforms, Laplace transforms and applications to partial differential equations. Additional topics may include an introduction to generalized functions. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.

Full details for MATH 5220 - Applied Complex Analysis

Introduction to the fundamentals of numerical analysis: error analysis, approximation, interpolation, and numerical integration. In the second half of the course, we use these to build approximate solvers for ordinary and partial differential equations. Strong emphasis is placed on understanding the advantages, disadvantages, and limits of applicability for all the covered techniques. Computer programming is required to test the theoretical concepts throughout the course. Students will be expected to be comfortable writing proofs and have knowledge of programming.

Full details for MATH 5250 - Numerical Analysis and Differential Equations

Combinatorics studies discrete structures arising in mathematics, computer science, and many areas of application. Key topics include counting objects with specific properties (e.g., trees) and proving the existence of structures (e.g., matchings of all vertices in a graph). We cover basic questions in graph theory, including extremal graph theory (how large a graph must be to have a certain subgraph) and Ramsey theory (large objects are forced to have structure). An introduction to network flow theory and variations on matching theory, including theorems of Dilworth, Hall, König, and Birkhoff, are discussed. Methods of enumeration (inclusion/exclusion, Möbius inversion, and generating functions) are applied to problems of counting permutations, partitions, and triangulations. Students will be expected to be comfortable writing proofs. More experience with proofs may be gained by first taking a 3000-level MATH course.

Full details for MATH 5410 - Introduction to Combinatorics I

MATH 6110-MATH 6120 are the core analysis courses in the mathematics graduate program. MATH 6110 covers abstract measure and integration theory, and related topics such as the Lebesgue differentiation theorem, the Radon-Nikodym theorem, the Hardy-Littlewood maximal function, the Brunn-Minkowski inequality, rectifiable curves and the isoperimetric inequality, Hausdorff dimension and Cantor sets, and an introduction to ergodic theory.

Full details for MATH 6110 - Real Analysis

This course emphasizes the "classical" aspects of partial differential equations (PDEs) — analytic methods for linear second-order PDEs and first-order nonlinear PDEs – without relying on more modern tools of functional analysis. The usual topics include fundamental solutions for the Laplace/Poisson, heat and wave equations in n dimensions, mean-value properties, maximum principles, energy methods, Duhamel's principle, and an introduction to nonlinear first-order equations, including shocks and weak solutions. Additional topics may include Hamilton-Jacobi equations, Euler-Lagrange equations, similarity solutions, transform methods, asymptotics, power series methods, homogenization, distribution theory, and the Fourier transform.

Full details for MATH 6150 - Partial Differential Equations

Covers measure theory, integration, and Lp spaces.

Full details for MATH 6210 - Measure Theory and Lebesgue Integration

Topics include existence and uniqueness theorems for ODEs; Poincaré-Bendixon theorem and global properties of two-dimensional flows; limit sets, nonwandering sets, chain recurrence, pseudo-orbits, and structural stability; linearization at equilibrium points: stable manifold theorem and the Hartman-Grobman theorem; and generic properties: transversality theorem and the Kupka-Smale theorem. Examples include expanding maps and Anosov diffeomorphisms; hyperbolicity: the horseshoe and the Birkhoff-Smale theorem on transversal homoclinic orbits; rotation numbers; Herman's theorem; and characterization of structurally stable systems. Prior exposure to topology (e.g., MATH 4530) will be helpful.

Full details for MATH 6260 - Dynamical Systems

MATH 6310-MATH 6320 are the core algebra courses in the mathematics graduate program. MATH 6310 covers group theory, especially finite groups; rings and modules; ideal theory in commutative rings; arithmetic and factorization in principal ideal domains and unique factorization domains; introduction to field theory; tensor products and multilinear algebra. (Optional topic: introduction to affine algebraic geometry.)

Full details for MATH 6310 - Algebra

An introduction to the theory of noncommutative rings and modules. Topics vary by semester and include semisimple modules and rings, the Jacobson radical and Artinian rings, group representations and group algebras, characters of finite groups, representations of the symmetric group, central simple algebras and the Brauer group, representation theory of finite-dimensional algebras, and Morita theory.

Full details for MATH 6330 - Noncommutative Algebra

Lie groups, Lie algebras, and their representations play an important role in much of mathematics, particularly in number theory, mathematical physics, and topology. This is an introductory course, meant to be useful for more advanced topics and applications. The relationship between Lie groups and Lie algebras will be highlighted throughout the course. A different viewpoint is that of algebraic groups. We will endeavor to discuss this along with the smooth viewpoint. Some knowledge of differential and algebraic geometry are helpful.

Full details for MATH 6390 - Lie Groups and Lie Algebras

An introduction to enumerative combinatorics from an algebraic, geometric and topological point of view. Topics include, but are not limited to, permutation statistics, partitions, generating functions and combinatorial species, various types of posets and lattices (distributive, geometric, and Eulerian), Mobius inversion, face numbers, shellability, and relations to the Stanley-Reisner ring.

Full details for MATH 6410 - Enumerative Combinatorics

MATH 6510-MATH 6520 are the core topology courses in the mathematics graduate program. This course is an introduction to geometry and topology from a differentiable viewpoint, suitable for beginning graduate students. The objects of study are manifolds and differentiable maps. The collection of all tangent vectors to a manifold forms the tangent bundle, and a section of the tangent bundle is a vector field. Alternatively, vector fields can be viewed as first-order differential operators. We will study flows of vector fields and prove the Frobenius integrability theorem. We will examine the tensor calculus and the exterior differential calculus and prove Stokes' theorem. If time permits, de Rham cohomology, Morse theory, or other optional topics will be covered.

Full details for MATH 6520 - Differentiable Manifolds

An introduction to topological K-theory and characteristic classes. Topological K-theory is a generalized cohomology theory which is surprisingly simple and useful for computation while still containing enough structure for proving interesting results. The class will begin with the definition of K-theory, Chern classes, and the Chern character. Additional topics may include the Hopf invariant 1 problem, the J-homomorphism, Stiefel-Whitney classes and Pontrjagin classes, cobordism groups and the construction of exotic spheres, and the Atiyah-Singer Index Theorem.

Full details for MATH 6530 - K-Theory and Characteristic Classes

Measure theory, independence, distribution of sums of iid random variables, laws of large numbers, and central limit theorem. Other topics as time permits.

Full details for MATH 6710 - Probability Theory I

Covers theory of effectively computable functions; classification of recursively enumerable sets; degrees of recursive unsolvability; applications to logic; hierarchies; recursive functions of ordinals and higher type objects; generalized recursion theory.

Full details for MATH 6840 - Recursion Theory

Covers topological vector spaces, Banach and Hilbert spaces, and Banach algebras. Additional topics selected by instructor.

Full details for MATH 7130 - Functional Analysis

Talks on various methods in scientific computing, the analysis of their convergence properties and computational efficiency, and their adaptation to specific applications.

Full details for MATH 7290 - Seminar on Scientific Computing and Numerics

Selection of advanced topics from number theory. Course content varies.

Full details for MATH 7370 - Topics in Number Theory

Selection of advanced topics in combinatorics. Course content varies.

Full details for MATH 7410 - Topics in Combinatorics

Selection of topics from algebraic geometry. Content varies.

Full details for MATH 7670 - Topics in Algebraic Geometry

Learning theory has become an important topic in modern statistics. This course gives an overview of various topics in classification, starting with Stone's (1977) stunning result that there are classifiers that are universally consistent. Other topics include classification, plug-in methods (k-nearest neighbors), reject option, empirical risk minimization, Vapnik-Chervonenkis theory, fast rates via Mammen and Tsybakov's margin condition, convex majorizing loss functions, RKHS methods, support vector machines, lasso type estimators, low-rank multivariate response regression, random matrix theory, topic models, latent factor models, and interpolation methods in high dimensional statistics.

Full details for MATH 7740 - Statistical Learning Theory

A twice weekly seminar in logic. Typically, a topic is selected for each semester, and at least half of the meetings of the course are devoted to this topic with presentations primarily by students. Opportunities are also provided for students and others to present their own work and other topics of interest.

Full details for MATH 7810 - Seminar in Logic

Supervised research for the doctoral dissertation.

Full details for MATH 7900 - Supervised Reading and Research