An Introduction to Cryptography: From the Caesar Cipher to the One Time Pad and Beyond – Pat Boland (FULL)
How do we transmit private information in a secure, yet feasible way? This question has challenged humans for thousands of years and has become increasingly more important with the technological advances of the 20th and 21st centuries. This course will study a number of cryptographic techniques and the mathematics used to implement and analyze each. We will attempt to pay homage to the work of former University of Michigan undergraduate student Claude Shannon in his development of modern cryptographic theory. For example, we will ponder: What technique should we use if the “enemy” knows the system? Mathematically we will introduce and use elements of combinatorics, probability and statistics, modular arithmetic, elementary number theory (including factorization as a means to study the RSA algorithm), and the concept of random number generation. This course will be interactive with a focus on group work and scholar presentations. We will also use the University computer labs to help implement and analyze ciphers.
An Introduction to Ecological & Micrometeorological Instrumentation – Cheyenne Lei (FULL)
How does a precipitation gauge record rainfall? Do you know how a wind vane measures the 3 dimensional wind vertices? How do we measure plant productivity and stress? How do we determine soil moisture for irrigation? Modern meteorology includes a wide variety of in situ instruments that are designed to observe aspects of our atmospheric environment, yet many of these instruments remain a mystery in their implementation and use. This course bridges the gap in introductory weather and climate, and ecology centered on commonly used micrometeorological instrumentation through hands-on assignments. Topics will include direct and indirect temperature measurements, rainfall, wind, plant chlorophyll and soil moisture. Each section will also discuss how each topic is important to the changing climate, how it ties into STEM careers for students.
Catalysis, Solar Energy and Green Chemical Synthesis – Corey Stephenson and Corinna Schindler (FULL) “Catalysis, Solar Energy, and Green Chemical Synthesis” will provide a fun and intellectually stimulating hands-on experience that instills a historical appreciation for the giants whose trials and tribulations have enabled our modern understanding of chemistry and biology. Students will learn modern laboratory techniques including how to set up, monitor, and purify chemical reactions, and most importantly, how to determine what they made! Experiments include the synthesis of biomolecules using some of the most transformative reactions of the 20th century and exposure to modern synthetic techniques, such as the use of metal complexes that absorb visible light to catalyze chemical reactions; an important development in the “Green Science” movement. Finally, industrial applications of chemistry such as polymer synthesis and construction of photovoltaic devices will be performed. Daily experiments will be supplemented with exciting demonstrations by the graduate student instructors.
Climbing the Distance Ladder to the Big Bang: How Astronomers Survey the Universe – Minh Nguyen (FULL)
The furthest objects that astronomers can observe are so distant that their light set out when the Universe was only 800 million years old; the light from these objects has been traveling to us for about 13 billion years. Even the Sun’s neighborhood – the local part of our Galaxy, where astronomers have successfully searched for planets around other stars – extends to hundreds of light years. How do we measure the distance to such remote objects? Certainly not in a single step! Astronomers construct the so-called “Distance Ladder,” finding the distance to nearby objects, thus enabling those bodies to be understood and used as probes of yet more distant regions. This class will explore the steps in this ladder, using lectures, discussions, field trips, and demonstrations. Students will learn basic computer programming, culminating in a project to model the motion of massive bodies interacting gravitationally. We will go to a nearby “mountain” near Ann Arbor to do night-time observing, guided by members of a local amateur astronomers’ club. We will cover concepts involving space, time, and matter that go far beyond the distance ladder, and involve some of the most fascinating mysteries in cosmology and astrophysics: What is it like inside a black hole? What is the Dark Matter? What is the Dark Energy that makes the Universe expand faster and faster? Is there other life in the Universe? The class is recommended for students with solid high-school mathematics background, including some exposure to vectors.
Dissecting Life: Human Anatomy and Physiology – Mary Orczykowski (FULL)
What are the systems of the human body and how do they work together to allow us to exist in the world? How can unique adaptations in animals teach us more about ourselves? In Dissecting Life, students will work together to learn the complexities and wonders of the human body through comparative anatomy dissections, observation of anatomy in action, case discussions, and studying plastinated and osteological anatomical donors within the University of Michigan Medical School’s Gross Anatomy Laboratories. Through this course, students will learn gross anatomy in detail and gain a basic understanding of physiology and histology as a foundation to study form and function.
Forensic Physics – Ramon Torres-Isea (FULL)
A fiber is found at a crime scene. Can we identify what type of fiber it is and can we match it to a suspect’s fiber sample, for example from a piece of clothing? Likewise, someone claims to have valuable ancient Roman coins, a newly-found old master painting, or a Viking map of America predating Columbus’ voyage. Are they authentic or fakes? How can we determine that using some physics-based techniques? (These are real examples the Viking map proved to be a forgery). Also for example, how is a laser-based molecular-probing technique used to stop criminals from trading billions of dollars of counterfeit pharmaceuticals and endangering thousands of lives? These are a few among many examples of experimental physics methods applied to several areas of Forensics. In this session, students will be introduced to these methods and have opportunities to make measurements using molecular, atomic and nuclear forensic techniques. In addition, applications to medical imaging and diagnostics will be introduced. Students will be working at our Intermediate and Advanced Physics Laboratories with the underlying physics for each method presented in detail, followed by demonstrations and laboratory activities, which include the identification of an “unknown” sample. Various crime scenes will challenge students to select and apply one or more of the methods and use their Forensic Physics skills to conduct investigations.
From Nuclei to Particles: Physics at the Smallest Scales – Jianming Qian (FULL)
Ever wonder how stars produce their energy? How did the Universe evolve in its first second? What are the fundamental building blocks of Nature? How do particles interact with each other? How do we study physical phenomena at the shortest distances? These are example questions that this course will try to answer. The course will be divided into three distinct but related subjects: nuclear physics, standard model of particle physics, and particle-matter interaction and detection. We will begin with a short introduction of modern physics, followed by discussions of topics in nuclear physics including nuclear stability and decays, energy generation through nuclear fission and fusion processes, and nucleosynthesis. We will then go over the standard model (SM) of particle physics, introducing quarks and leptons and reviewing major discoveries that led to the development of the SM. Finally, we will survey techniques and tools for studying physics at the smallest scales including particle accelerators and radiation detectors.
Graph Theory – Doug Shaw (FULL)
Ignore your previous knowledge of algebra, geometry, and even arithmetic! Start fresh with a simple concept: Take a collection of points, called vertices, and connect some of them with lines called edges. It doesn’t matter where you draw the vertices or how you draw the lines – all that matters is that two vertices are either related, or not. We call that a “graph” and you’ve taken the first step on the Graph Theory road! Graphs turn up in physics, biology, computer science, communications networks, linguistics, chemistry, sociology, mathematics- you name it! In this course we will discuss properties that graphs may or may not have, hunt for types of graphs that may or may not exist, learn about the silliest theorem in mathematics, and the most depressing theorem in mathematics, learn how to come up with good algorithms, model reality, and construct some mathematical proofs. We will go over fundamental results in the field, and also some results that were only proved in the last year or so! And, of course, we will present plenty of currently unsolved problems for you to solve and publish!
It’s in my DNA: From Gene to Protein – Anati Azhar and Hector Mendoza (FULL)
Have you ever heard the phrase “it’s in our DNA?”. This inspirational concept is commonly used to describe unique qualities and behaviors that make a person successful: honesty, courage, integrity, etc. But from a scientific perspective, what exactly does this expression mean? In this two-week course, we are going to embark on a journey of discovering exactly how DNA holds the blueprint for an organism and how this blueprint is interpreted. In the first week, we will review the structure and function of DNA during interactive lectures, complemented with exhilarating laboratory experiments that will challenge students’ investigational processes and creativity to maximize comprehension of the material. In the second week of the course, students will be introduced to the processes through which DNA is transformed into RNA and protein. These two molecules are crucial to understand how and why life “looks” a certain way. A great analogy to understand the flow of genetic information is to think of DNA as a cookbook, with many recipes (RNA) that give rise to many different dishes (proteins). Get your aprons and utensils ready, and let’s get cooking!
Sustainable Polymers – Anne McNeil (FULL)
From grocery bags and food packaging to contact lenses and therapeutics, there is no doubt that polymers have had a positive impact in our lives. Most of these polymers are made from petroleum-based feedstocks, which are dwindling in supply. And although some plastics are recycled, most of them end up contaminating our lands and oceans. Through hands-on lab work and interactive lessons, this class will introduce the future of polymer science – that is: polymers made from sustainable materials that ultimately biodegrade! Students will conduct research experiments to make, analyze, and degrade renewable plastics. We will also examine commercial biodegradable materials and plastics used for energy and environmental remediation, and practice science communication through a creative stop-motion animation project.
The Geometry of Music – Alessandro Danelon (FULL)
Math and music are related in multiple ways. From the Western historical point of view we find connections in the math of Pythagoras, in the development of the equal temperament, and in the theoretical and artistic work of Iannis Xenakis. One can use group theory to phrase music structures, and both mathematicians and musicians claim the creative process as the moving power of their discipline. Composers used symmetries in their compositions, and scientists tried to associate sounds to their objects of study according to their inner mathematical structure. The aim of this course is to highlight some geometric and algebraic structures in the theory of music. We will start reviewing musical notions like scales, intervals, triads, harmonic progressions, tonality, modality and harmonic rhythm together with the physics of the sound (pitch and frequencies). We will then study the geometry of pitch organization and transposition and move on to explore the harmonic structure and harmonic structure of a phrase, together with the geometry of chromatic inversions. At this point we revise musical scales and intervals with geometric tools and move on to discover the geometry of harmony: Riemann’s Chromatic inversions, and Euler’s Tonnetz. On the algebraic side, we will introduce groups, their theory, and use their language in the theory of music. We will also discuss how a deeper understanding of the underlying music can help us in improving our playing and performances. Performers are encouraged to bring their instruments.