## Course Advice

Hear what students have to say about the trendiest classes around.

## 5 Series

__Physics 5A__ — Introductory Mechanics and Relativity (3)

**Physics 5A explores basic tenets of classical mechanics, espousing fundamental principles about how things move, collide, turn, wave, and flow. The end of the course also features discussion of special relativity, the theory governing the behavior of objects moving at close to the speed of light. While oft-described by students as more mathematically strenuous than Physics 7A, it is also an excellent preparation course for upper division physics courses.**

*“For mechanics, I'd really recommend spending a lot of time on oscillation because it comes off too often everywhere else. But since the 5 series is relatively new, I think it should be mentioned that it is pretty helpful to have 53 concurrently with 5A because of the math background.”* – Teresa Du, undergraduate physics

*“I think the most salient piece of advice is definitely just to tell people to do work in the reading room right? It's where you find people to help you with the problem sets, and it's where you find friends.”* – Clay Halbert, undergraduate physics/philosophy

*“Take the 5 series and if it’s totally overwhelming then you can easily drop to the 7 series (other way around is more difficult but people still do it). PS most people feel overwhelmed by the 5 series… find some friends to study with.”* – Katie Latimer, physics/chemistry alumna

*“The vast majority of this course is about mechanics but in a very challenging way. The last two weeks are about special relativity. The questions on problem sets and exams will almost always require single variable calculus (both differentiation and integration). These are significantly harder than the ones you see in Physics C AP Mechanics. Recommended only for intended physics/astrophysics/engineering physics majors who have taken AP Physics C Mechanics.”* – Andrew Hsu, undergraduate physics/astrophysics

__Physics 5B__ — Electromagnetism, Waves, and Optics (3)

**An introductory electromagnetism course which explores Maxwell’s equations relating electric and magnetic fields to charge and current distributions. The class also explores the wave equation and foundational optics, including topics such as geometric optics and interference. Physics 5B is a difficult class primarily directed towards physics majors, although physics-passionate non-majors are welcome. While Physics 7B also fulfills the lower division electromagnetism requirement, Physics 5B is very recommended for physics students looking for success in upper division courses and beyond.**

*“LEARN SUPERPOSITION.”* – anonymous

*“The vast majority of this course is about electricity and magnetism but in a very challenging way. The last three weeks is waves and optics (Snell’s Law). The questions on problem sets and exams will be significantly harder than the ones you see on Physics C Electricity and Magnetism. Lots of multivariable calculus will be required. Recommended for people who have taken Physics 5A and have Physics C AP background.”* – Andrew Hsu, undergraduate physics/astrophysics

*“Physics 5B is an excellent but challenging class covering the basics of electricity and magnetism as well as waves and optics. Compared with 7B, 5B covers more material and in greater depth, meaning that it moves much faster and is generally more difficult and time-consuming; in exchange, you will achieve a deeper conceptual understanding by taking 5B and you will have more exposure to ‘thinking like a physicist.’ Students have much greater access to the professor in 5B but actually receive more individual attention overall in 7B, since time with the GSI per week is 4 hours (plus office hours) for 7B, versus 1 hour (plus office hours) for 5B, and the sections for 7B are usually smaller. 5B is very much aimed at likely physics majors, which means that the professor may assume that it is one of the highest priorities among your courses for the semester. If the class is not, in fact, a high priority, then 7B might be a better choice; even if you later decide to major in physics, it is absolutely possible to succeed having taken 7B. On the other hand, if the class is a high priority (because you plan to major in physics, or because that’s a strong possibility, or because you just find physics really exciting to study) and you are willing to put in the time, you will get a lot out of 5B and it is likely worth giving it a try. It is also worth noting that, unlike with 7B, the difficulty and workload of 5B will vary tremendously with the instructor and GSI(s). Finally, don’t be afraid to go meet with said instructor/GSI(s)—they can help you decide whether 5B or 7B is a better option based on your individual background and priorities.”* – Physics 5B GSI

__Physics 5BL__ — Introduction to Experimental Physics I (2)

**An introductory laboratory class which is generally paired with Physics 5B. The class explores the basics of various aspects of experimental physics through hands-on labs about various topics such as mechanics, sound, and circuits. Students are introduced to concepts such as error propagation and develop the skills associated with writing lab reports.**

*“This course is meant to be taken together with Physics 5B. This is a required course for Physics and Astrophysics major if you are not taking Physics 7B. The first one-third of this course is about printing out about 15 pages of paper your instructor provided and filling them out as you do the lab. The other two-third of the course is split roughly evenly between mechanics and Electricity and Magnetism labs. You will write the lab reports on a lab notebook. One person from each lab group of 3 will be randomly selected to get graded on their work. That person’s grade will become every group member’s grade. Beware of the mid-semester quiz about error propagation and some handling of uncertainties, it is not easy.”* – Andrew Hsu, undergraduate physics/astrophysics

__Physics 5C__ — Introductory Quantum Mechanics and Thermodynamics (3)

**Many students’ first brush with the two vast fields of quantum mechanics and statistical mechanics. Students in Physics 5C will spend a large amount of time acquainting themselves with solutions to the Schrödinger equation, a revolutionary law of nature which governs the movement and evolution of things in the quantum world. The latter half of the course shifts to statistical mechanics, which is a way to tease out the behavior of a large number of objects where the dynamics are intractable. Rather than rehashing over phenomenological thermodynamics principles, Physics 5C introduces the derivation of our familiar thermodynamics laws with what logic which essentially amounts to counting.**

*“With Aganagic, it was the first time she was teaching the class and there was no official syllabus. So the class was a weird mix of 137A and stat mech, at an advanced level. Only for the most theoretical people, who want a challenge. [Expect] out of 5C, a solid understanding of Stat mech and Quantum at Griffiths level.”* – Physics 5C GSI

*“With Dan Kasen, the first half of the course is quantum mechanics and the second half is thermodynamics. The last week is about combining those two together. A different professor might reverse the order. I personally find the quantum mechanics exam questions and problem sets in this course to be harder than the 137A upper division quantum mechanics material. Therefore it would be a good idea to take 137A and this course concurrently so that you have a better introduction to quantum mechanics material. Recommended only for people who have previously taken both Physics 5A and 5B/5BL.”* – Andrew Hsu, undergraduate physics/astrophysics

__Physics 5CL__ — Introduction to Experimental Physics II (2)

**The second introductory laboratory class which is generally paired with Physics 5C. Students gain experience working with experimental setups by performing various labs related to optics, modern physics, and thermodynamics, among others. The course concludes with a capstone project in which students demonstrate their newfound experimental competence via a group lab report and presentation.**

*“This course is required for physics/astrophysics major if you are taking the 5 series and not taking Physics 7C. This course is meant to be taken with Physics 5C. In addition to writing up lab reports on a lab notebook, a group also has to submit an electronic (usually using latex) lab report(which is weighted more in the final grade). One person from each lab group of 3 will be randomly selected to be graded for their physical lab notebook, which his/her score will be the entire group’s grade. Majority of 5CL is about optics (6 labs), one lab on photoelectric effect, two labs on thermodynamics, and one final project that relates to those topics. Each group will do a demo and presentation of their final project in the last week of lab.”* – Andrew Hsu, undergraduate physics/astrophysics

## 7 Series

__Physics 7A__ — Physics for Scientists and Engineers (4)

**(...)**

*“7A was pretty fun to be in since it was not too hard to grasp all the content that was taught in the class while showing some of the kinematics and statics basics needed to understand basic problems. Problem sets aren’t great since they’re all online, but they were never impossibly hard or super time consuming, so I’d recommend this class if you just want to try an easier physics class.”* – Jackson Le, undergraduate civil and environmental engineering

__Physics 7B__ — Physics for Scientists and Engineers (4)

**(...)**

__Physics 7C__ — Physics for Scientists and Engineers (4)

**(...)**

## Lower Division

__Physics 77__ — Introduction to Computational Techniques in Physics (3)

**(...)**

*“Do not procrastinate starting 77 homework, start in it immediately. It will always take a lot longer than you think it will.”* – Arani Acharya, undergraduate physics

*“This course is basically a computer science class for physics majors. It gives us an introduction to programming in python jupyter notebook in ways that are applicable to doing physics experiments. There are weekly programming assignments and one final project. You must show up to every lecture (2 hours per week) and workshop (2 hours per week taught by GSI) to get full participation grade. Every student (whether working by himself or with one or two other group members) will present their final project and show a demo in dead week.”* – Andrew Hsu, undergraduate physics/astrophysics

__Physics 89__ — Introduction to Mathematical Physics (4)

**This class covers a variety of physically useful mathematical concepts. The class explores such topics as linear algebra (the incredibly useful study of anything “linear”), tensor analysis (where students learn to bypass extensive computations with index notation), complex analysis (an inquiry into an amazing extension of the familiar real numbers), Fourier and Laplace transforms (the dissection of all signals into pure tones), and others. Physics 89 tackles these topics with a practical slant, focusing less on the mathematical rigor of each argument and more on applications of newfound mathematical tools to physics.**

*“This course is a replacement of Math 54 for Physics and Astrophysics majors. The skills you learned in this class are the foundational math skills you need for all upper division physics classes.”* – Andrew Hsu, undergraduate physics/astrophysics

*“I would say that in a sense Physics 89 was among the most useful I've taken at Berkeley; at least with Austin Hedeman I found that the material kept coming in handy again and again throughout my undergrad career.”* – anonymous

## Upper Division Requirements

__Physics 105__ — Analytic Mechanics (4)

**Physics 105 may sound like a rehashing of lower division classical mechanics but, at its heart, is a fundamentally groundbreaking course. Students explore the Lagrangian and Hamiltonian formulations of classical mechanics which apply the curiously named “principle of least action” to transform the messy vector equations of Newtonian vector mechanics into the elegant scalar relations of analytic mechanics. Students will see how the centrifugal and Coriolis forces fall beautifully out of the math of rotating frames, how central force potentials manifest as gravitational orbits, and how vibrations and rotations can be treated under this new analytical framework. Instructors also often introduce the basic concepts of chaos theory, a field which attempts to describe systems whose dynamics are extremely sensitive to initial conditions. This course is a must-have for even the least classical-sounding physics fields out there.**

*“It’s been hypothesized that the pace and content of this class vary greatly every semester. You might call this class ‘7A on steroids’, but every bit of new technique and model will be presented in a more systematic and rigorous fashion. Taylor’s textbook is also pleasant to read and exercise with. If you want even more thorough preparation, Landau’s mechanics is usually waiting for you in the physics library. In general, mastery of 105’s content, especially Hamiltonian mechanics, perturbation methods and central potential scattering, can make it a lot easier to transition into 112 and 137A.”* – Yourong “Frank” Wang, undergraduate physics/mathematics

*“Collaboration with others can be key in the homework, but exams and key concepts should be independently absorbed. Thus, while you may bounce ideas with classmates for assignments, make sure you readily understand what you're doing and practice by yourself.”* – Nijaid Arredondo, undergraduate physics/astrophysics

__Physics 110A__ — Electromagnetism and Optics (4)

**This course is essentially an extension of the lower division electrodynamics of Physics 5B/7B. In this class, students will make a significantly deeper dive into the apparently familiar theory of electromagnetism through a higher level of vector calculus. The class explores in depth the macroscopic formulation of Maxwell’s equations which describe the laws of electrodynamics in realistic materials that respond to electromagnetic fields. The familiar electric and magnetic fields can be thought to arise from scalar and vector potential functions which introduce the fancy-sounding concept of a “gauge theory.” On this note, the class segues into a more rigorous exploration of special relativity in a way that reveals the deeper geometrical interpretation of the theory.**

*“There is a lot of overlap between 110A and 5B. Topics that are not covered in 5B include techniques for solving Laplace equations, auxiliary fields, Lorenz gauge and vector potential. Uniqueness theorem and symmetry arguments are sometimes useful for simplify calculations. Making comparisons between electricity and magnetism will also help understanding the concepts better (e.g., multipole expansion for the potentials, and bound charge and current, etc.). Make sure you are familiar with Stokes' theorem and divergence theorem from multivariable calculus as you will be using them quite often to derive equations in lectures. Note that although the class is called Electromagnetism and Optics, 110A doesn't deal with optics at all. 110A is known to be one of the easiest physics upper divs, so in my opinion it's good to start your upper divs with this class, any time after you're done with 5B/7B, 53, and 89.”* – Youqi Song, undergraduate physics

__Physics 111A__ — Instrumentation Laboratory (3)

**Physics 111A, previously 111BSC (basic semiconductor circuits), has a notorious reputation for the vast amount of time it requires. With (or without) a partner, students learn the basic theory behind increasingly complicated circuits while heading into the Donald A. Glaser laboratory on the second floor to put those theoretical ideas to practice. While in the class, students will learn to produce and readout signal parameters. It is impossible to come away from the course without a reasonable understanding of diodes (which “pump” current in one direction), JFET and BJT transistors (the basis of switches), op amps (which magnify voltages insanely), and analog/digital logic. The course also introduces students to the National Instruments software LabVIEW, which is used in countless physics labs across the world. The course culminates in a final project where students’ creativity and circuit-building prowess are put to the test. As a rite of passage of the physics major, one should heed the warning/advocacy: tread wisely.**

*“Physics 111A: The key in this class is to be ON TOP OF YOUR GAME for the first three labs or so, then the rest will still be hard and unpleasant but at least you won’t be extraordinarily stressed out about being behind schedule. It’s helpful to have some basic clue about how circuit elements work but beyond that just follow the directions. If you are able, taking this over the summer will require a very concentrated effort over that one summer, but will free you up to concentrate more effectively on coursework over the year (I did 111A and research over the summer at the sacrifice of any semblance of social life or really free time at all and in retrospect am glad I made the decision).”* – Katie Latimer, undergraduate physics

**Also offered in the summer.**

__Physics 111B__ — Experimentation Laboratory (3)

**(...)**

*“Physics 111B: This class is only as fun as you make it. Pick labs based on 1) how interested you are in the subject, followed by 2) availability and time constraints. If you’re into what you’re working on you’ll have an OK time. But the lab reports are horrible. Plan to be constantly working on at least one lab report at all times during the semester you take 111B. Also: read the lab manual before coming in. That’s not a joke or a suggestion.”* – Katie Latimer, physics/chemistry alumna

__Physics 112__ — Introduction to Statistical and Thermal Physics (4)

**(...)**

*“Apparently this class will always be taught by Charman from now on. The first third of the class is about classical thermodynamics, concluding with a midterm about classical thermodynamics. The rest of the course is statistical mechanics. Charman will teach some 105 and 137A stuff in lectures as well as some basic Bayesian statistics. Don’t worry if you didn’t do well on one of his tests, the average is (historically) low (below 50%) anyway and he will make the exams you do well weight more than the exams you didn’t do so well in the final grade. His problem sets are long and can be challenging but people still get very high percentage on problem sets.”* – Andrew Hsu, undergraduate physics/astrophysics

*“I took 112 with Holzapfel and it was hands down the most eye-opening physics class I have taken. One of my favorite moments in the class was deriving the ideal gas law ( PV = NkT) from scratch and it was so simple and elegant. The homework could be long and algebra-laden at times, and Taylor expansion and various other approximations will become your best friend. I’d honestly take it again just for fun. To me it was the upper div physics class that required the least difficult math, but I did suck at 137/linear algebra so take my advice with a grain of salt?”* – Aini Xu, undergraduate physics/computer science

__Physics 137A__ — Quantum Mechanics (4)

**As a first pass at introductory quantum mechanics for most students, Physics 137A is a truly mind-blowing course which reveals the fundamental weirdness governing the universe. One can expect to learn quantum mechanics through its various formulations to describe the ever elusive “wavefunction,” which governs the inherently probabilistic dynamics of quantum systems. Using the all-important Schrödinger equation, Physics 137A explores what happens to particles in free space, infinite wells, and quadratic “harmonic oscillator” potentials, among others. The class uses lessons from these toy models to derive the level scheme of the hydrogen atom from basic principles. In addition, the class explores the uncanny valley produced by the at-once intuitive and elusive concept of spin, a discussion which yields to an example of quantum entanglement.**

*“Apparently this class will always be taught by Charman from now on. The first third of the class is about classical thermodynamics, concluding with a midterm about classical thermodynamics. The rest of the course is statistical mechanics. Charman will teach some 105 and 137A stuff in lectures as well as some basic Bayesian statistics. Don’t worry if you didn’t do well on one of his tests, the average is (historically) low (below 50%) anyway and he will make the exams you do well weight more than the exams you didn’t do so well in the final grade. His problem sets are long and can be challenging but people still get very high percentage on problem sets.”* – Andrew Hsu, undergraduate physics/astrophysics

*“Feynman famously said ‘I think I can safely say that nobody understands quantum mechanics.’ You should ignore this quote despite its famous source, just as you should ignore the sci-fi technobabble in which quantum mechanics is invoked to explain all manner of bizarre things. Both encourage a view of quantum mechanics as magic that is utterly wrong-headed. In fact, quantum mechanics is rigorous and one of the best-understood areas of physics—otherwise it would not be part of the standard undergraduate curriculum! You will not be hopelessly confused, nor will you unlock the mysteries of the universe. Mostly you’ll do a lot of linear algebra and a lot of integrals, and you’ll solve a few differential equations. Other than having this correct mindset that quantum mechanics is rigorous understandable science and not a magic black box, my main advice to a new student planning to take 137a is to make sure you know your linear algebra. If you’ve taken something like math 110, you’re in great shape, but you can get by with math 54. Also, get access to Wolfram Mathematica if you don’t already have it—it will make your life much easier. (Professors can sometimes get the physics department to provide a license to the students in a class, so ask about this!)”* – Physics 137A GSI

**Also offered in the summer.**

__Physics 137B__ — Quantum Mechanics (4)

**Whereas Physics 137A discusses fundamental postulates of quantum mechanics and simple toy models, Physics 137B equips the connoisseur of “real physics” with the ability to handle real systems with clever tools. After picking up inventive approximate methods such as perturbation theory (for small changes to a potential), the variational principle (for estimating energies of intractable systems), and WKB theory (for slowly varying potentials in certain regimes), students will be able to handle systems as diverse and practical as the helium atom, atomic level transitions, and nuclear decay. The class also addresses identical particles as well as scattering, increasing the class’ portfolio of useful lessons. Depending on the instructor, this class may also provide an introduction to quantum information or other special topics.**

*“Bousso is theoretical. Crommie is great. Crommie is more experimental, but covers all of Griffiths. Class is not rushed, good pace, great homeworks. Exams not too hard at all. Bousso goes too fast, just to talk about information and qubits. The class is harder. [Expect] out of 137B, actual tools in quantum to tackle problems people care about today.”* – Physics 137B GSI

## Upper Division Electives

__Physics 110B__: Electromagnetism and Optics (4)

**(...)**

*“This course is offered every semester. This course will generally follow Griffiths chapters 9 – 12. However, in chapter 9 (EM waves), Griffiths only considers transverse waves and not longitudinal. Depending on the professor, they may discuss both longitudinal and transverse modes in media, which they might refer to some texts aimed at the graduate level like Jackson or Zangwill to fill the gaps in that Griffiths left out. Depending on the professor’s interests / research, certain topics may be emphasized more than others. For instance, if the course was taught from a condensed matter perspective, in that special relativity, 4-vectors, covariant notation will be introduced but not emphasized, whereas various aspects of light and matter interaction will be emphasized more.”* – Stephen Ebert, physics alumnus

__Physics 129__ — Particle Physics (4)

**A thrilling elective, Physics 129 provides the framework for thinking about high-energy physics. After tackling relativistic formulations of quantum mechanics, Physics 129 quickly dives into a first-pass at the bizarre intricacies of quantum field theory, uncovering, along the way, the mathematical origin of spins, antiparticles, and the fundamental forces. The class caps off with a candid mathematical sketch of the sensationalized, mass-giving Higgs mechanism and a description of the standard model. Depending on the dispositions of the instructor, Physics 129 can either take an extremely theoretical focus or emphasize experimental considerations and data analysis.**

*“Particle physics is a perfect training ground for applying everything you know about quantum physics and special relativity. While you can learn a lot of theory up to electroweak unification and the standard model if you’re interested, the course also pays significant attention to simulation and data analysis. A very interesting elective.”* – Yourong “Frank” Wang, undergraduate physics/mathematics

**Only offered in the fall.**__Physics 138__: Modern Atomic Physics (3)

**(...)**

**Only offered every other spring.**

__Physics 139__ — Special Relativity and General Relativity (3)

**(...)**

*“I was on the fence about taking this class initially but now feel that it’s almost essential for physics majors - especially if you haven’t taken much astro (like me). It’s just totally different (both in terms of mathematical tools and physical ideas) from really any of the other core classes and plus you learn about black holes so what’s not to love?”* – Katie Latimer, physics/chemistry alumna

**Only offered in the spring.**__Physics 141A__ — Solid State Physics (4)

**(...)**

*“Curriculum will be highly dependent on the professor. Qiu was great in my own opinion (it’s his area of expertise). Generally regarded as an easier elective but probably want to have at least one of (if not both) 137A or 112.”* – Katie Latimer, physics/chemistry alumna

*“141a: This class is a really good introduction to the field of condensed matter physics and is crucial if you are interested in pursuing that field. Depending on the professor different topics will have heavier emphasis, but you will learn all the basics to crystals, electric properties of materials, among other important basics to understanding condensed matter physics. Having taken it with Analytis, he was a fantastic lecturer that cared about helping the students understand the topics and graded the class very fair, as well as going into the right amount of depth in each topic. In terms of prerequisite courses, 137B can be taken concurrently, but some points in the course will be more difficult if done. 112 is not a prerequisite, but it will make the class easier. There are a couple weeks of the class that heavily use 112 topics and if you have not taken 112 you will need work harder to better understand these sections, but it is definitely possible to do. Overall, a great class if you are interested in the subject and in general a fair course.”* – Jake Byron, physics alumnus

__Physics 141B__ — Solid State Physics (3)

**(...)**

*“141b: This class goes into much more depth than 141a and can be a great resource for understanding more complex parts of condensed matter physics research, however it can be very confusing. Often times the class has many graduate students, during my time about 1/2 of students were grad students. The class, in my experience, goes over many topics not discussed in 141a, looking at magnetic materials in depth, BCS theory on superconductivity, and gives a look into contemporary research going on in the field. Depending on the professor, the difficulty and workload will vary quite a bit, but in general the grading tends to be pretty generous. If you are serious about doing condensed matter, or a close enough related field (material science, electrical engineering, etc) this course is super useful. Over all, a good class that really gives you a deep knowledge of the field, however can be very difficult to understand given the depth that the course dives to.”* – Jake Byron, physics alumnus

**Only offered in the spring.**

__Physics 151__ — Elective Physics: Special Topics (3)

**The topic of this class varies from semester to semester, and generally covers a relatively specialized field, often one in which the instructor has specific expertise. Physics 151 topics are generally disclosed and advertised before the semester starts. The rapidly changing focus of the class means that students should expect to be more flexible with regard to impromptu deviations from the syllabus, though its specific dives into interesting subjects often makes it a very rewarding experience.**

Past topics:

- Fall 2017(2): Noise In the Real World (
*B. Sadoulet*) - Fall 2017(1): Data Science and Bayesian Statistics for Physical Sciences (
*U. Seljak*) - Spring 2018: Quantum Information and Computation (
*H. Häffner*) - Fall 2017: Data Science and Bayesian Statistics for Physical Sciences (
*U. Seljak*)

__Physics 177__ — Principles of Molecular Biophysics (3)

**(...)**

__Physics C191__ — Quantum Information Science and Technology (3)

**(...)**

**Sporadically offered.**

## Astronomy

__Astronomy 7A__ — Introduction to Astrophysics (4)

**(...)**

*“The focus of these classes [Astronomy 7A/B] is on the math and physics behind astro, at an intro level; it is far more quantitative than qualitative. The classes are extremely helpful preparation for upper division astro classes as they go over the fundamental physics behind concepts that are essential for upper-div astro classes like stellar physics and cosmology, as well as introducing the curricula of those classes. People intending to major in astro would therefore strongly benefit from taking these classes, although they are considered optional for the major.”* – Samantha Wu, applied mathematics/astrophysics alumna

*“Astro 7A really prepared me for research in the astronomy department and reaffirmed my decision to go into astrophysics. It was also a well-taught class with lots of resources to take advantage of.”* – Makena Fetzer, undergraduate astrophysics

*“It introduced me to a more order-of-magnitude reasoning style which was a great extension to the more formal and rigorous physics curriculum.”* – anonymous

**Only offered in the fall.**

__Astronomy 7B__ — Introduction to Astrophysics (4)

**(...)**

*“7B is a really fun class, and I learned a lot while GSI-ing for it. 7B is very useful in learning astrophysics ‘culture’ and thinking like an astrophysicist, which I think is a big takeaway of the class (beyond just learning the material that's taught.) By astrophysics culture, I mean there's a big emphasis on things like order of magnitude estimates, dimensional analysis, and ‘observables/directly measurables’ (e.g. distance to a galaxy—not observable; angular separation on sky—observable). To elaborate a bit more on the above, although being comfortable with math and being able to do physics is crucial to being successful in astrophysics, the way you learn to think in an astrophysics class is quite different from a physics class. Astrophysics requires you to be clever in a different way than physics (e.g. how do you measure the distance to that galaxy?), and 7B is a good introduction to that. The material is challenging, not because you have to learn crazy hard math, or do incredibly complex calculations, but because you have to apply all sorts of different concepts from your calculus and intro physics classes at the same time, in a single problem-- having to mix together lots of concepts is what tends to trip up people. If you major in astrophysics, you will certainly take more upper division classes for the detailed derivations and excruciating/complex details, and 7B serves as a great framework for which you can add those details on. If you don't major in astrophysics, but you know calculus and mechanics, and are interested in how the universe works, you would also enjoy 7B. Also, after the 7A/B series, you should be able to go to the weekly astronomy colloquium and have some idea of what the speaker is talking about. Lastly, GSI life advice (for this class and many others.) The GSIs and professors want to help you—come to office hours! Ask us for help if you're struggling—earlier is better than later! Making sure you know how to do the derivations and homework without reference/help is important-- it serves as a great test to whether you really understand the material. A tip from Eugene was to redo your homework with a blank piece of paper, and I'd suggest doing something similar with the derivations. Do not ‘cheat’ by referencing your old homework/notes to get a hint or to check whether you got an intermediate step right! Having to come up with it yourself is key.”* – Astronomy 7B GSI

**Only offered in the spring.**

__Astronomy 120__ — Optical and Infrared Laboratory (4)

**(...)**

**Only offered in the fall.**

__Astronomy 121__ — Radio Laboratory (4)

**(...)**

*“Why take radio astronomy? CAUSE IT’S AWESOME. It provides the background you need to do research in radio astronomy. You get to learn how a radio telescope works from the ground up--to the point where if you had the materials, you could probably build one. Then, once you've done that, you get to learn how MULTIPLE radio telescopes work together to get an even better pictures of the sky. And all along you learn how to analyze and interpret the data coming in from the telescopes, figuring out what the hydrogen line is, how to find the orion super bubble, and how to determine the temperature of the moon and the sun. What advice can I give? The course is taught in python. Having experience in python definitely helps. Also a lot of time has to be put into the labs and lab write-ups. Expect at least 8 hours per writeup and 12-20 hours per lab, and the possibility of having to do certain parts of the lab twice either because you find the data is not sufficient, or was taken incorrectly (there are four labs total). It’s a given that having good lab partners helps, so if you find yourself in the situation where you are struggling to work well with your group, talk to a GSI or the professor. If you have no experience in astronomy, it might require a little more work at the beginning of class to get familiar with some vocabulary, but most of the class is self-contained so you should still be able to succeed in the course! That being said, Physics 111A helps with understanding how all the measurement tools and analog components work, so consider taking that course before taking this course.”* – Guillaume Shippee, undergraduate physics/astrophysics

**Only offered in the spring.**

__Astronomy 128__ — Astronomy Data Science Laboratory (4)

**(...)**

**Only offered in the spring.**

__Astronomy 160__ — Stellar Physics (4)

**(...)**

*“As this is an upper division astro class, it relies on the students having a foundation in core physics, primarily thermodynamics and quantum mechanics. Having knowledge of particle physics can also be helpful, but the curriculum will review all of these concepts. The class will go in depth into the physics of stars - their structure and evolution over their lifetimes. For people interested in pursuing post-undergrad studies in astrophysics, this class is extremely good preparation as it gives insight into topics that actually come up in astro research nowadays. For people just looking to study in undergrad, it’s an extremely interesting class and a great capstone to all the physics and astro learned in the major thus far. There is not a consistently helpful text for this class so going to office hours and taking good lecture notes will be extremely beneficial.”* – Samantha Wu, applied math/astrophysics alumna

**Only offered in the spring.**

__Astronomy C161__ — Relativistic Astrophysics and Cosmology (4)

**This class covers the fundamentals of cosmological physics. The class begins with a brief overview of general relativity and elaborately explores topics such as the Friedmann-Robertson-Walker metric, big bang nucleosynthesis, inflation, and large scale structure. Astronomy C161 is for the student seeking introduction to the field centered around answering deep questions about the birth and evolution of the universe.**

**Only offered in the spring.**

__Astronomy C162__ — Planetary Astrophysics (4)

*“As taught by Imke, the class can surprise you as you don’t know what you don’t know and it is very easy to get points taken off on homeworks and midterms. Any word questions asking you to describe why something is the way it is, is tricky. The formulas you will encounter in the class are tricky as well since you need to be aware of what those variables are. There are weekly problem sets and 2 midterms. No final exam because there is a term project where you do research on any solar system astrophysics topic you came up.”* – Andrew Hsu, undergraduate physics/astrophysics

**Only offered in the fall.**

## Mathematics

__Mathematics 53__ — Multivariable Calculus (4)

**A foundational multivariable calculus course which explores such useful concepts as partial derivatives, non-Cartesian coordinate systems, and multiple integrals. The crown jewels of the course are the fundamental theorem of line integrals as well as Green’s, Stokes’s, and the divergence theorems, which are all insightful generalizations of the fundamental theorem of calculus. Math 53 is a must for physics majors, who must grapple with such vector calculus-heavy subjects as electrodynamics.**

*“I would say that 53 is probably taken as soon as possible, because even 5A uses some concepts such as spherical coordinates and line integrals.”* – Teresa Du, undergraduate physics

*“Beware of the weekly quizzes during discussion. The curve for Math 53 is tougher than the Physics department so it is even more important to be ahead of the curve. Fear not, the competition in Math 53 is inferior to that of Physics classes so you will be at an advantage. Unlike the Physics Department, the homeworks are graded on completion not on accuracy so you can write made up answers on HW if you don’t have time.”* – Andrew Hsu, undergraduate physics

**Also offered in the summer.**

__Mathematics 54__ — Linear Algebra and Differential Equations (4)

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*“I took 54 and 89 at the same time. Pros: reinforcement for similar material, learn the math more solidly while getting to know physical applications. Cons: math requires more strict ways of doing things. Especially diffy q's. My math GSI definitely did not like separation of variables.”* – Teresa Du, undergraduate physics

*“It’s okay.”* – Kevin Hu, undergraduate electrical engineering and computer sciences

**Also offered in the summer.**

__Mathematics 55__ — Discrete Mathematics (4)

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*“Discrete Mathematics (Math 55) at Berkeley is a great course that foremost teaches you about writing rigorous mathematical proofs; a necessary skill for proceeding further with mathematics. The main objects of study in Math 55 are discrete; you will learn how to calculate probability for discrete events, how to model problems using graphs, and use graph theoretic techniques to gain insight. It is a good idea to take this class if you are looking for an introduction into mathematical rigor; for instance if you are having trouble understanding the mathematical reasoning of higher level textbooks. It is also a good class to take for learning typesetting (LaTeX) if you are new to it; as it offers many formal proofs that can be typeset up.”* – Joshua Lin, undergraduate mathematics/physics

**Also offered in the summer.**

__Mathematics 104__ — Introduction to Analysis (4)

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*“Introduction to Analysis (Math 104) at Berkeley represents an undergraduate's introduction into higher level formal analysis. In this class, you can expect to take concepts that you once only understood informally (like the denseness of the rationals in the reals); and begin to be able to formalise these concepts. The main object of study for this course is the real number system, its construction and functions over it. Math 104 is a gateway to further understanding of mathematical rigor and formalisation; and highly recommended for anyone considering further study in mathematics. In this class, you will have much more practice with proofs, which the main means of communication between mathematicians. As a last note; oftentimes people draw a distinction between informal arguments (often made in physics) and rigorous arguments (made in maths). It is definitely true that to be able to argue informally; one must first be able to argue formally, c.f. Terence Tao.”* – Joshua Lin, undergraduate mathematics/physics

**Also offered in the summer.**

__Mathematics 110__ — Linear Algebra (4)

**An extension to the linear algebra curricula of Math 54 and Physics 89. Math 110 reviews the linear algebra uncovered by its lower division prerequisite in a more extensive fashion than 54 and with a more rigorous treatment than 89. In Math 110, the focus is placed on the abstract theory of vector spaces rather than algorithms for matrix manipulation, leading to a rich discussion of the beautiful structure of linear things. While much of Math 110 is theoretically review, the course includes such novel topics as an elegant generalization of diagonalization called Jordan canonical form and an introduction to quadratic forms, a linear object untouched by prerequisite classes.**

*“110 will lay foundations for all of the physics you will ever do.”* – anonymous

**Also offered in the summer.**

__Mathematics 113__ — Introduction to Abstract Algebra (4)

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*“Take math 113 if you want exposure to some group theory and want to make some deep connections that are beyond the scope of what is typically expected in the undergraduate physics courses.”* – anonymous

**Also offered in the summer.**

__Mathematics 121A__ — Mathematical Tools for the Physical Sciences (4)

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**Only offered in the fall.**

__Mathematics 121B__ — Mathematical Tools for the Physical Sciences (4)

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**Only offered in the spring.**

__Mathematics 128A__ — Numerical Analysis (4)

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**Also offered in the summer.**

__Mathematics 128B__ — Numerical Analysis (4)

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**Only offered in the spring.**

__Mathematics 185__ — Complex Analysis (4)

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*“Stuff you learn in 185 is useful in surprising situations.”* – anonymous

*“Math 185: Introduction to some beautiful and useful systems on the complex plane. Some of the fundamentals are directly beneficial to physics majors in terms of technique and theorems. Certainly a very interesting maths class and sometimes very photogenic (with e.g. Riemann Surfaces).”* – Yourong “Frank” Wang, undergraduate physics/mathematics

**Also offered in the summer.**

## Non-major

__Physics 8A__ — Introductory Physics (4)

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*“From my own personal experience (I had DeWeese for 8A), I would strongly recommend reading the chapters in the book before coming to lecture (read about the topic before it's lectured on). That's something I didn't do until later in the semester and it probably saved me from getting a lower grade. Make sure [you] have a general idea of derivatives and integrals.”* – anonymous

*“Go over homework problems with one or two friends in a small study group. Working through problems in a group like this helped me not only learn both concepts as well as different problem solving techniques much better, but also gave me a support system for when Physics got rough.”* – Natalie Musick, undergraduate integrative biology

**Also offered in the summer.**

__Physics 8B__ — Introductory Physics (4)

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**Also offered in the summer.**

__Physics C10__ — Descriptive Introduction to Physics (3)

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**Sporadically offered.**

__Astronomy C10__ — Introduction to General Astronomy (4)

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*“Astronomy C10 is an introductory course in astronomy without any prerequisites. This course is perfectly suitable for students from other fields than physics or other science majors, but students can also take this course as a preparation for upper courses in lieu of Astronomy 7 series. The course covers a large range of materials, from the solar system to cosmology, and the material is phenomenon based and not math heavy. There are several interesting labs and one selective field trip included.”* – anonymous

*“It is a relatively easy class, but taking it was a great decision. Filippenko really engages with his students and getting to discuss his work with him was extremely eye-opening.”* – Jonathan Li, undergraduate applied mathematics

**Only offered in the fall.**

__Astronomy C12__ — The Planets (4)

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**Only offered in the spring.**

**Also offered in the summer as “Astronomy W12.”**

__Physics C21__ — Physics and Music (3)

**The Physics of Music is a class which applies principles such as physics and the fundamentals of sound to the study of music. The course exhibits numerous insightful demos and explores the nature of music with only basic algebra and geometry. It is geared towards students who are studying subjects other than physics, and is certainly quite friendly to non-majors of all kinds.**

*“Of course, I do think the course was designed for students who have little to no knowledge on physics. That they shouldn’t be afraid of any crazy mathematical equations of any of kind. I definitely was able to learn concepts that surrounded music, as someone who sang and plays an instrument, it definitely taught me to view music from a different perspective, but now I see music from a better understanding. Of course the student doesn’t need musical training either. The projects were the definitely the most fun for me. It gave me the opportunity to be creative and explore themes that I was curious about, like I researched different kinds of bird singing, and my second one was why some people, when they sing, can sound nasal-ish. The quizzes were reasonable and were definitely given ample time to study, a student is given the tools and enough office hours (I visited many times) and the professor along with his GSIs were very approachable and helped expand my ideas on the projects.”* – Cynthia Garcia, undergraduate social welfare

**Offered sporadically.**