There is no problem of the week for the rest of this semester. We are having trouble coming up with a 5 series level problem that is unique. You(anyone in the world who is reading this) are welcomed to send an email to ucbsps@gmail.com titled Problem of The Week Suggestion in which you write out both the problem and the solution that we should put on here next semester. It must be original, unique, and not easily searchable in the internet.

Below will be a complete list of all problem solvers of the week in history.

SPS Problem solvers of the week | |

Mouseover the table for Problem solver Pictures/Profiles | |

The Society of Physics Students is a professional, national organization for all students interested in physics. We are the chapter at University of California - Berkeley. We outreach, promote and discuss physics in our meetings, tour lab facilities such as Lawrence Livermore National Lab and the Advanced Light Source, and connect with professors and their research via bi weekly student faculty lunch. This upcoming school year we will be posting weekly problems and after at least a few days the solution will be shown. We will also do some student seminar in our weekly general meetings. We also support an FAQ at the bottom of this page to give advice about physics courses and the physics major, and we have a course guide at the bottom of the page. We are working on collecting more students thoughts about all physics and related discipline courses and will update our course guide and FAQ accordingly. We are a student group acting independently of the University of California. We take full responsibility for our organization and this web site. Any questions, comments, or feedback or interested in getting involved? Email us at ucbsps@gmail.com. If you have a weekly question in mind please email us. Interested in getting involved? Subscribe to our mailing list by emailing ucbsps@gmail.com State your name and any email you want to get subscribed.

The Society of Physics Students is an organization dedicated to physics-related ideas and cutting-edge research. We encourage and assist students interested in physics to develop the knowledge, competence, enthusiasm, and social responsibility that are essential to the advancement of physics; stimulate interest in advanced study and research in physics; develop collegiality among physics students and faculty members; promote public interest in physics; and provide liaison between students and the member societies of the American Institute of Physics.

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**What’s the difference between the 5 series and the 7 series? If I already classes in one of these, can I switch to the other mid-sequence?**

There are several notable differences between the 5 series and the 7 series, listed below: Whereas the 7 series problem sets are infamously conducted using Mastering Physics, 5 series problem sets are more tailored to hone skills useful in upper division physics. In general, 7 series classes tend to be populated by students of many different disciplines including engineering fields whereas the 5 series classes are almost completely populated by physics majors. Despite covering similar topics, the curricula of the two sequences differ in important ways. Special relativity is taught in 5A and 7C. Thermodynamics is covered in 7B and 5C, and, in the latter of the two classes, emphasis is placed on statistical mechanics rather than classical thermodynamics. Optics is a subject handled by 5B and 7C. While the 7 series includes a built-in laboratory section where each course is 4 units, 5 series classes are 3 units but are paired with the (separate) 2 unit laboratory classes Physics 5BL and Physics 5CL (Introduction to Experimental Physics I/II). 7 series labs usually involve filling out worksheets but include more self-contained lab reports towards the end of the sequence. 5 series labs start off being somewhat worksheet-based in the beginning of 5BL and evolve to complete lab reports by the end of 5BL and 5CL. It is entirely possible (and precedented) to switch between the two sequences if desired. However, because of curriculum mismatches, students are sometimes required to take 1 supplementary unit covering the material that they would miss in the new sequence (under the coursename Physics 49). For example, students switching from 7A to 5B were required to take Physics 49 to satisfy the lower division relativity requirement.

**What are Physics H7A/B/C and how can I take them?**

The Physics H7 series was the honors introductory physics series primarily geared towards physics majors. It has since been phased out and replaced by the Physics 5 series, which serves a similar purpose but features a rearranged curriculum and more extensive parallel laboratory courses.

**What is the 8 series?**

The 8 series (Physics 8A/B) is the lower division introductory physics sequence for certain non-physics fields such as MCB (molecular and cellular biology) and architecture, among others.

**Do I have to take Math 54? Can I take Math 54 in place of Physics 89?**

Math 54 is not a physics requirement in most circumstances. While it never hurts to ask, the physics department has historically been very unlikely to allow Math 54 in place of Physics 89 unless the petitioning student is a double major in mathematics—the math department does not allow Physics 89 in place of Math 54, and the physics department will allow Math 54 if the student is double-majoring in math. This confusion has caused many students to have to take Physics 89 after already having taken Math 54. However, some students report that Math 54 in its own right is a good introduction to/review of linear algebra, which is also covered in Physics 89.

**What is Physics 89 and how is it different from Math 54?**

Physics 89, like Math 54, handles the topics of introductory linear algebra and differential equations. However, unlike Math 54, Physics 89 focuses less on rigorous proofs and more on applications in physics—the eigenvalue problem is often almost immediately related to coupled spring systems, for example. Physics 89 also often covers such topics as basic tensor manipulations, Fourier and Laplace transforms, complex analysis, and Green’s functions, although the exact curriculum is semester- and professor-dependent.

**Is there any specific order to take classes in?**

There are a few guidelines for what order to take physics classes in: Lower division classes should be taken before upper division classes. Some students take upper division physics classes concurrently with their later lower division classes, although this is not necessary. Lagging letters in course numbers indicate an order in which classes should be taken (i.e., you should take “Physics 137A” before “Physics 137B”), although some exceptions exist. You should generally take prerequisites/co-requisites for a class before/concurrently with that class (although the listed prerequisites are not always necessary; check with your peers who have taken the class before). Aside from these, there is a lot of freedom to sculpt exactly how you go about completing the physics major requirements. In your upper division coursework, you will have the ability to take classes in almost whatever order you want.

**Does the 5 series count in place of the 7 series for insert major here?**

The 5 series is just essentially the “honors” version of the 7 series, and there is no reason why any department would not allow this substitute. Among others, the astrophysics and EECS majors have accepted the 5 series without question.

**What are Physics 111A/B and when should I take them?**

Physics 111A (BSC, basic semiconductor circuits) is a famous (infamous?) circuit laboratory class which is required for all physics majors. Students explore various mostly practical aspects of circuitry, generally with a lab partner. It is famously a very time-consuming course, requiring many hours during the normal semester and even more during the summer sessions, where the pace of the class is greatly accelerated. It is our most sincere recommendation not to take this class alongside too many other technical classes: though it is not “difficult” in the traditional sense, it is extremely demanding on time. Many students also swear by taking the class during the summer; even though the pace is very fast, students are often unburdened from other academic responsibilities and can focus on succeeding both in 111A and in the regular school year. Physics 111B is quite different from 111A in that, rather than exploring basic aspects of circuit design, students perform historical, often Nobel-winning experiments. Students who have taken the course report that Physics 111B is very demanding for a few select weeks out of the semester when a lab is due, but is otherwise different in nature from 111A. While there is no single good answer for when to take this class, many students opt to take it their senior year since it is not really prerequisite for anything else. This class does not need to be taken immediately after 111A.

**Should I take a graduate class?**

If you are an undergraduate, you should really only consider taking a graduate class if you have exhausted the undergraduate classes in a topic and are genuinely interested in moving forward. Bad reasons to take grad classes as an undergrad include: My friends are doing it I want to look smart I want to impress grad schools (on the list of things they care about, this is at rock bottom) I want to fulfill a corresponding upper division major requirement (the physics department doesn’t accept these) If you’re a graduate student, um, yeah, you should take grad classes. They’re called grad classes—they’re exactly what it says on the tin.

**Why should I join SPS?**

Unlocking the secrets of the universe is fun, but it’s even more fun with friends. Also, we have snacks.

**How can I join SPS?**

If you want to be a part of SPS, then you already are. Aside from our mailing list (which you can contact us to join) and officer rolls, we do not keep a formal roster of people who are a part of this club. Some students opt to join SPS National, which requires membership dues of $24 per year but provides various benefits such as membership in the American Physical Society and another physics organization of one’s choosing, though most members are not a part of SPS National and it is certainly not prerequisite to being a part of the club in any way.

**How can I become an officer of SPS?**

Constantly show up at our meetings and activities and volunteer throughout the year. Nominate yourself in April officer nomination, make a campaign speech, and then vote for yourself in our Annual officer election in late April.

**How can I get involved in SPS?**

Outside of weekly meetings, our chapter of SPS facilitates a variety of activities including regular barbecues, faculty-student lunches, outreach events, occasional professional development sessions and panels, and laboratory tours. We are always looking for proactive members to volunteer for these kinds of events. Doing so is a great way to get involved with us and meet a bunch of awesome people who love the same stuff that you do.

**What happens at SPS meetings?**

At SPS meetings, we make important announcements often followed by some other kind of professional/fun activity. In the past, we have Paired underclassmen with upperclassmen in a mentorship arrangement Provided course advice on a variety of classes Given research presentations Given presentations about giving research presentations In addition, among other things, we have Played board games Had a spooky scavenger hunt Made Valentine’s Day cards for our amazing physics advisors Exchanged gifts in the annual “Secret Schrödinger” tradition Climbed to the sixth floor of Campbell Hall (unimpressive) Climbed up to the Big C (more impressive) Gathered in a lecture hall to watch Spongebob (most impressive) If that isn’t enough incentive to attend, we even provide snacks! This alone should be incentive!

**Do I have to be a physics major to be a part of SPS?**

No. We will love you anyway <3

**Why should I be a physics major?**

Non-exhaustive list of good reasons to major in physics: You want to know how the universe works You like doing math to solve problems that actually exist in real life or at least in theory in real life You like hanging out with people who go to social gatherings and continue to talk about what they study and think about during the day The thought of going on in your life and no longer doing physics makes you a little sad You love physics Non-exhaustive list of bad reasons to major in physics: You want people to think you’re smart You want people to remember your name after you’re dead (they probably won’t) You want to win a Nobel Prize (you probably won’t) You already told people you’re going to but now you realized it isn’t really your thing but you’re afraid if you switch majors people will judge you (that’s on them) You want to make money (that’s a funny joke)

**Do I apply to Berkeley as a physics major? How can I declare a physics major? How can I declare a second major?**

The physics major falls under the College of Letters and Science. This means that, while you may apply indicate an intended major on your application, you will come into the school undeclared. In order to declare the physics major, you must either have completed or be enrolled in your lower division physics requirements after the drop deadline for that semester. You can declare the physics major by going to the third floor of LeConte and talking to our wonderful physics advisors. However, be aware that the engineering physics major is under the College of Engineering, where students may apply and be admitted straight into a major. To declare a second major, you need to satisfy all the requisite lower division requirements for both majors (and whatever requisite GPA cap needed for the second major, if any), fill out a double major declaration form and have advisors from both departments sign it. You will then need to bring it to 206 Evans Hall, whereupon bureaucracy takes over, and you should expect to see your majors on CalCentral within days/weeks.

**Is there a GPA requirement to declare the physics major?**

Unlike for relatively impacted majors at Berkeley like computer science or statistics, the physics major does not have a particularly strict GPA cap. There is a lower division 2.0 minimum GPA requirement to declare, although this is not a particularly stringent restriction. There is also an overall 2.0 GPA requirement to graduate, although this requirement is schoolwide and not specific to the physics major in particular.

**Do I need to be good at math to become a physics major?**

Honestly, this is a tough question. Physics inevitably includes a large amount of math when describing physical phenomena. While algebra, (single and multivariable) calculus, and linear algebra are absolutely essential in succeeding as a physics major, other fields of math such as group theory and complex analysis, among others, also occasionally get involved. All of this is the truth. However, you aren’t really expected to be a master all the math needed to do physics right at the beginning, in the same way that you aren’t expected to know all of physics before becoming a physics major. You can, and usually will, learn the math as you go. The defeatist attitude of thinking you are “bad at math” is often over-pessimistic and self-defeating (yes, really!), though “liking” (or, at least, being okay with the idea of doing math) is pretty necessary.

**Am I smart/hardworking/dedicated enough to do a physics major?**

Yes. If we can believe in you, then you can believe in yourself.

**Should I double major?**

You should double major if you really like the subject that you are double-majoring in. Students in physics commonly double major in subjects such as mathematics, astrophysics, computer science, and many others. However, do not feel obligated to get a double major just to get the credential—it is much better (and easier!) to focus on a single subject you love than to drag yourself through many second major course requirements because you feel like you have an obligation to. Certainly, physics graduate school does not expect you to have a double major.

**Why is my degree a Bachelor of Arts?**

The physics major at Berkeley falls under the College of Letters and Science, which exclusively provides Bachelor of Arts degrees. However, professional organizations do not care about this and will treat it just like any other physics degree. For the three of you who still care about this: don’t.

**How do I get research? Do I need to do research?**

There is no single way that undergraduate students get research. There are many campus resources such as the Undergraduate Research Apprentice Program (URAP) and the Berkeley Physics Undergraduate Research Scholars Program (BPURS) and ULAB, among others. However, emailing professors/postdocs/graduate students or visiting them during office hours is a very common way to get into research. Programs such as research experiences for undergraduates (REUs) allow for short research opportunities over the summer, although they require relatively early applications. Generally speaking, if your aim is to get into grad school, research tends to be regarded as quite critical because it provides exposure to “real physics” (as opposed to “lecture-midterm-final physics”). In addition, graduate schools often require three letters of recommendation, and professors who are writing for students who have worked with them are usually better equipped to write strong letters of recommendation. However, this should not be seen as a rush to get started on research—it is very common to defer research until sophomore year. Research does not have to be done every semester and, for undergraduates, is almost always ultimately non-committal (there is no shame in leaving a group because you do not find the research area interesting).

**What is research like?**

While all research opportunities are different, there is a common theme for most positions. Generally, you will be assigned to some graduate/postdoctoral mentor who will show you the ropes. Oftentimes, you will be assigned basic tasks at first, during which you start to understand the research group’s dynamics as well as its area of interest. While you won’t necessarily be expected to contribute too much at first, you may find that you will gradually take on greater responsibility the longer you stay in the group. Exactly when/how this happens depends on your particular circumstances.

**What do I have to do in order to get into grad school?**

The????????????

**Do I have to go to grad school?**

Absolutely not! Many physics students actually go into industry right out of college. There are many ways to be successful with a physics degree! One caveat, however, is that it is very difficult to find a job in the field of physics itself without some kind of graduate degree, although the analytical skills provided by the physics degree are applicable in places other than physics. It sometimes feels like there is a stigma against not going to grad school, but this is honestly pretty silly. As cheesy as it sounds, no across-the-slate one-size-fits-all path really exists because there are many ways to succeed (the irony of this claim is recognized). Even if you go into decide to go into industry and change your mind down the line, you can still go to grad school.

**I just thought of this theory that gravity is magnetism and the work-energy theorem is wrong and that I have refuted/overturned/revolutionized/unified GR/quantum mechanics/thermomechanicalmagnetohydromechanicoplasmaparticle-ology. Who can I email to collect my Nobel Prize?**

Sorry, we’d really like to help you out, but we aren’t really the people to contact about that. Please forward those emails to Stanford.

**Prerequisites:** Math 1A; Math 1B(concurrent) or equivalent

**Format:** 3 units; 3 hr lecture, 2 hr discussion.

**Grading:** B average, 1-2 midterms, final, assignments.

**Topics:** The vast majority of this course is about mechanics but in a very challenging way. The last two weeks is special relativity. Use of calculus and vector algebra is emphasized. Topics include Kinematics, dynamics, work and energy, rotational motion, oscillations, some fluids. The questions on problem sets and exams will be significantly harder than the ones you see on Physics C AP. Recommended for intended physics, astrophysics, engineering physics majors who have AP Physics C background.

**Textbooks:** Kleppner, An introduction to mechanics (textbook might vary based on professor)

**Comments:** This course is relativily new, first offered Fall 2016.
“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 and chemistry alumnus
“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

**Prerequisites:** Physics 5A or 7A(consult with advisor) and Math 53(concurrent)

**Format:** 3 units; 3 hr lecture, 2 hr discussion.

**Grading:** B+ average, 1-2 midterms, final, assignments.

**Topics:** 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. Use of multivariable calculus and vector algebra is emphasized. Topics include Electric fields and potential, circuits, magnetism and induction, waves, light propagation, relection, refraction and interference. The questions on problem sets and exams will be significantly harder than the ones you see on Physics C AP. Recommended for intended physics, astrophysics, engineering physics majors who have AP Physics C background and took 5A.

**Textbooks:** Purcell, Electricity and Magnetism (textbook might vary based on professor)

**Comments:** This course is relativily new, first offered Spring 2017
“LEARN SUPERPOSITION.”
“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

**Prerequisites:** Physics 5A or 7A, and 5B or 7B(concurrent)

**Format:** 2 units; 2 days of lab every week, 2.5 hours each.

**Grading:** B+ average, 1 quiz, the rest is labs.

**Topics:** This course is required for physics/astrophysics major if you choose to take the 5 series. It is recommended that one take this course concurrent with 5B. The first one-third of the course is about printing out about 15 pages of paper your instructor provided and filling them out as yyou do the lab. The other two-third of the course is split between mechanics and E & M labs and you will write up lab reports on a lab notebook. One person from each lab group (of 3) will be randomly selected to get graded on their work. The person's grade will become every group member's grade.

**Textbooks:** None

**Comments:** This course is relativily new, first offered Spring 2017
“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 (describing the course as taught by Bordel)

**Prerequisites:** Physics 5A and 5B or 7A and 7B(consult with advisor, 5 and 7 series topics are different) and Math 54 or Physics 89(concurrent)

**Format:** 3 units; 3 hr lecture, 2 hr discussion.

**Grading:** B/B+ average, 1-2 midterms, final, assignments.

**Topics:** About half of the course is Thermodynamics, half quantum mechanics. Which comes first depends on the professor. Use of calculus and linear algebra is emphasized. Topics include Temperature, kinetic theory, entropy; particle/wave duality, Schrodinger equation, hydrogen atom, applications of quantum mechanics. Recommended for intended physics, astrophysics, engineering physics majors who took Physics 5A and 5B previously.

**Textbooks:** A.P. French Introduction to Quantum Physics(M.I.T. Introductory Physics Series) and Blundell, Concepts in Thermal Physics (textbook might vary based on professor)

**Comments:** This course is very new, first offered Fall 2017
“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

**Prerequisites:** Physics 5A and 5B and 5BL or 7A and 7B, and 5C or 7C(concurrent)

**Format:** 2 units; 2 days of lab every week, 2.5 hours each.

**Grading:** B+ average, based on labwork, attendance, 1 final project

**Topics:** This course is required for physics/astrophysics major if you choose to take the 5 series. It is recommended that one take this course concurrent with 5C and already took 5BL. In addition to writing up lab reports on a lab notebook a group also has to submit an online (latex) lab report (which is graded heavier). One person from each lab group (of 3) will be randomly selected to get graded on their work. The person's grade will become every group member's grade. Majority of the 5CL is about optics and some labs about thermodynamics, photoelectric effect. Each group will do a final project and presentation of a lab of their choice (within the topic of modern physics)

**Textbooks:** None

**Comments:** This course is relativily new, first offered Fall 2017

**About 7A:** Offered every semester in the school year, and during the summer.
“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

**About 7B:**

**About 7C:**

**About 8A:** Offered every semester in the school year, and during the summer.
“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.”
“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

**About 8B:**

**About C21:** 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.
Offered in the spring once every few years.
“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

**Prerequisites:** Math 1A or equivalent and Physics 5A or 7A(concurrent)

**Format:** 3 units; 2 hr lecture, 2 hr workshop/lab.

**Grading:** varies instructor to instructor, based on attendance, programming homework, and final project.

**Topics:** This course is recommended for physics majors because it teaches you python skills specifically for physics research. Topics include how to program visualization, statistics and probability, regression, numerical integration, (Monte Carlo) simulation, data modeling, function approximation, algebraic systems.

**Textbooks:** None (textbook might vary based on professor)

**Comments:** This course is relativily new (slightly older than 5A)
“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

**Prerequisites:** Math 1A; Math 1B or equivalent and Math 53

**Format:** 4 units; 3 hr lecture, 2 hr discussion.

**Grading:** B average, 2 midterms, final, assignments.

**Topics:** This course is similar to Math 54 but designed for physics majors. Any student who majors in physics must take this course. Topics include Complex numbers, linear algebra, ordinary differential equations, Fourier series and transform methods, introduction to partial differential equations, introduction to tensors. You will need all these mathematical tools for the upper division physics courses.

**Textbooks:** Boas, Mathematical Methods in the physical scineces (textbook might vary based on professor)

**Comments:** This course is relativily new, pioneered by Austin Hedeman
“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.”

**About 105:** 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.
Offered every semester in the school year.
“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/math
“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

**Prerequisites:** Physics 5ABC or 7ABC and Math 53

**Format:** 4 units; 3 hr lecture, 1 hr discussion. Problem set each week

**Grading:** B average, 1-2 midterms, final, assignments.

**Topics:** Review of vector calculus. Electrostatics (Coulomb's law, Gauss's law, electric potential, work & energy, capacitors). Solving Laplace's equation (Image charges, Separation of variables, multipole expansion). Electric fields in matter (Dielectrics, Polarization, Displacement field). Magnetostatics (Lorentz force law, Biot-Savart law, Ampere's law, Vector potential). Magnetic fields in matter (Magnetization, Auxiliary field). Electrodynamics (Ohm's law, Faraday's law, Inductance, Solving DC circuits, Maxwell equations) Conservation laws (Continuity equation, Poynting's theorem, Maxwell stress tensor). EM waves (Fresnel equations)

**Textbooks:** Griffiths - Introduction to Electrodynamics (good)

**Study-aides:** Study Aides: past tests (https://tbp.berkeley.edu/courses/physics/), Professor Qiu's Website (http://physics.berkeley.edu/research/qiu/teaching/110a/110a.htm)

**Comments:**
“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

**About 110B: **

**Prerequisites:** Physics 5ABC,5BL,5CL or 7ABC, Math 53, Math 54 or Physics 89

**Format:** 3 units; 8 hr lab, 3 hr lecture; 1 lab report on most weeks

**Grading:** B+ average, final project, lab reports

**Topics:** 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.

**Textbooks:** Horowitz,Hill - The Art of Electronics (good reference, class covers only a fraction of its contents)

**Study-aides:**http://socrates.berkeley.edu/~phylabs/bsc/

**Comments:** There are 12 (including final project) lab reports. Out of that only 5 are full reports and require > 7 hours to write up. The rest are either short reports, which take ~4 hours to finish, or notebook submissions which take < 1 hr to finish. Make sure you start early on the full reports. A good way to save time in the lab is to read the lab manual carefully, including the exercises, before coming to the lab.
“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, physics and chemistry alumnus

**About 111B: ** Offered every semester in the school year.
“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

**Prerequisites:** Physics 5ABC or 7ABC, Math 53, Math 54 or Physics 89

**Format:** 4 units; 3 hr lecture, 1 hr discussion. Problem set each week

**Grading:** B average, 1-2 midterms, final, assignments.

**Topics:** Statistics (Poisson distribution, Indistinguishability). Thermodynamics (Processes, 1st and 2nd law, heat capacity, efficiency & Carnot engines, Maxwell-Boltzmann distribution) Classical statistical mechanics(Boltzmann's definition of entropy, microcanonical ensemble, chemical potential, canonical ensemble, paramagnet model, Gibbs factor & Gibbs sum [Grand canonical ensemble], Equipartition theorem). Quantum Statistical mechanics (Blackbody radiation,Stefan's law, Debye specific heat, Ideal Fermi gas, Chandrasekhar limit, Ideal Bose gas, Bose-Einstein Condensate), Phase transitions(Ising model, Mean field theory, Critical exponents, Landau theory of phase transitions)

**Textbooks:** Kittel - Thermal Physics (moderate)

**Study-aides:** past tests (https://tbp.berkeley.edu/courses/physics/)

**Comments:** “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
empty
“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

**About 129: ** Offered in fall semesters.
“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/math

**Prerequisites:** Physics 5ABC or 7ABC, Math 53, Math 54 or Phyisics 89. Some people take Physics 5C concurrently with 137A

**Format:** 4 units; 3 hr lecture, 1 hr discussion. Problem set each week

**Grading:** B average, 1-2 midterms, final, assignments.

**Topics:** Topics: Failure of classical physics. Wave function (probability, normalization, wave particle duality, wave packets, wave function in momentum space, Heisenberg's uncertainty principle). Schrodinger's equation (Stationary states, Ehrenfest Theorem, potential step, well, barrier, delta function, harmonic oscillator, raising and lowering operators). Formalism (Operators & eigenfunctions, Dirac notation, matrix representation, Hermitian, unitary, projection operators, commutators, generalized uncertainty principle) Schrodinger in spherical polar coordinates(Orbital angular momentum, spherical harmonics, general angular momentum & spin, spin 1/2 systems & Pauli matrices, addition of angular momentum, radial solution, Hydrogen atom)

**Textbooks:** Griffiths - Introduction to Quantum Mechanics (good) or Bransden & Joachain - Quantum Mechanics (good)

**Study-aides:** past tests (https://tbp.berkeley.edu/courses/physics/), Bound states in different types of potentials (http://phet.colorado.edu/en/simulation/bound-states)

**Comments:**
“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

**Prerequisites:** Physics 5ABC or 7ABC, Math 53, Math 54 or Physics 89, Physics 137A

**Format:** 4 units; 3 hr lecture, 1 hr discussion. Problem set each week

**Grading:** B average, 1-2 midterms, final, assignments.

**Topics:** Identical Particles (two-particle wavefunctions, bosons, fermions), time-independent perturbation theory (degenerate theory, non-degenerate theory, fine structure, spin-orbit coupling, energy level corrections of hydrogen atom, Zeeman effect), Variational Principle, WKB approximation (classical region approximation, tunneling, connection formulas), time-dependent perturbation theory (two-level systems, sinusoidal perturbations, emission and absorption of radiation, Einstein's A and B coefficients, selection rules), adiabatic approximation (adiabatic theorem, berry's phase), Scattering (Classical and Quantum scattering theory, partial wave analysis, Born ap

**Textbooks:** Griffiths - Introduction to Quantum Mechanics (good) or Bransden & Joachain - Quantum Mechanics (good)

**Study-aides:** past tests (https://tbp.berkeley.edu/courses/physics/), notes (http://socrates.berkeley.edu/~jemoore/p137b/p137b.html)

**Comments:** “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

**About 139: ** Offered in spring semesters.
“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 and chemistry alumnus

**Prerequisites:** Physics 5ABC or 7ABC, Math 53, Math 54 or Physics 89, Physics 137A, (Physics 137B), Physics 112

**Format:** 4 units; 3 hr lecture, 1 hr discussion. Problem set each week

**Grading:** B+ average, 1-2 midterms, final, assignments.

**Topics:** Crystal Structure (periodic array of atoms, types of lattice), wave diffraction (reciprocal lattice, scattered wave amplitude, Brillouin zones, fourier analysis of basis), crystal binding (inert gases crystals, ionic crystals, covalent crystals, metals, hydrogen bond, elastic constants), phonons (vibrations of crystals with monoatomic and diatomic basis, quantization of elastic wave , phonon momentum, inelastic phonon scattering, phonon heat capacity, phonon thermal conductivity), free electron fermi gas (energy levels 1/2/3D, effect of temperature, heat capacity, electrical conductivity of electron gas, motion in magnetic field, thermal conductivity of metals), energy bands (nearly free electron model, bloch functions, kronig-penney model, crystal momentum of electron, central equation and approximate solutions, band gap, metals and insulators), semiconductors (holes, effective mass, bloch oscillator, intrinsic carriers, chemical potential, doping, p-n junctions, band bending, diodes), tight binding, plasmons and polaritons (screening, dielectric function, plasma optics, polariton dispersion)

**Textbooks:** Introduction to Solid State Physics - Kittel (okay for review, not great for explanations), Solid State Physics - Ashcroft and Mermin (excellent for explanations)

**Study-aides:** past tests (only one) (https://tbp.berkeley.edu/courses/physics/), practice problems (harder than standard problems) solid state physics: problems and solutions - Mihaly and Martin

**Comments:** “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 and chemistry alumnus
“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 Bryon, physics alumnus

**About 141B: ** Offered in spring semesters.
“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 Bryon, physics alumnus

**About 151: ** 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.
Generally offered every semester in the school year.
Past topics:
Fall 2017: Data Science and Bayesian Statistics for Physical Sciences (U. Seljak)
Spring 2018: Quantum Information and Computation (H. Häffner)
Fall 2018 (1): Data Science and Bayesian Statistics for Physical Sciences (U. Seljak)
Fall 2018 (2): Noise In the Real World (B. Sadoulet)

Take both Physics 89 and Math 54 if you are majoring in Math too. physics majors are required to take Physics 89 (instead of math 54).

Physics 89's prerequisite is Math 53. Either the 5 or 7 series satisfy physics or astrophysics majors.

Undergrads are not expected to take graduate classes but are encouraged to do so if you have taken the prereqs shown in the chart and want to fullfill your curiosity and/or prove to grad school you are capable of handling tough material.

Blue: Required courses for Physics Major Green: Graduate Courses Yellow: Elective Physics Orange: Required Labs

**Prerequisites:**Math 1A,1B or equivalent.

**Format:** 4 units; 3 hour lecture per week; 3 hour discussion

**Grading:**B- average, 2 in-class midterms, 1 final exam.

**Topics:**Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivaties. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes. This course required for Physics Major

**Textbooks:** Stewart Math 53 custom edition

**Study-aides:** N/A

**Comments:**“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

**Prerequisites:**Math 1A,1B or equivalent.

**Format:** 4 units; 3 hour lecture per week; 3 hour discussion

**Grading:**B average, 2 in-class midterms, 1 final exam.

**Topics:**Basic Linear Algebra; matrix arithmetic and determinants. Vector spaces; inner product spaces. Eigenvalues and eigenvectors; orthogonality, symmetric matrices. Linear second-order differential equations; first-order systems with constant coefficients. Fourier series, application to partial differential equations.

**Textbooks:** Differential Equations(Quick Study Academic)

**Study-aides:** N/A

**Comments:** “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 EECS

**Prerequisite s:** None

**Format:** 4 units; 3 hour lecture per week; 1 hour discussion; Problem set due every week.

**Grading:** B- average; 2 in-class midterms; 1 final exam.

**Topics:** (Logic and Proofs) - Propositional Logic, Predicates and Quantifiers, Rules of Inference, Introduction to Proofs. (Basic Structures) - Sets, Functions, Sequences, Summations, and Cardinality of Sets. (Number Theory and Cryptography) - Divisibility, Modular Arithmetic, Promes, Greatest Common Divisors, Congruences, and Cryptography. Strong/Structural Induction, Well-Ordering, and Recursion. (Counting) - Basics of Counting, Pigeonhole Principle, Permutations, Combinations, and Binomial Coefficients. (Discrete Probability) - Probability Theory, Bayesâ Theorem, Expected Value and Variance. Generating Functions, Inclusion-Exclusion, Chinese Remainder Theorem, and Euclidean algorithm. (Graphs) - Directed Graph, Bipartite Graphs, Adjacency Matrices, Undirected Graphs, Isomorphism, Euler and Hamilton Paths.

**Textbooks:** Discrete Mathematics and its Applications (Custom for UCB), 7th Edition by Kenneth Rosen (good)

**Study-aides:** N/A

**Comments:** For this class, make sure you understand all the material and definitions by heart, that way it is a lot easier to do proofs. Also, be sure you know how to do the different kinds of algorithms, such as the Chinese Remainder Theorem. The exams are mostly half proofs and half computational.

**Prerequisites:**Math 53, Math 54, and Math 55.

**Format:** 4 units; 3 hour lecture per week; 1 hour discussion; Problem set due each week.

**Grading:**B average, 1-2 in-class midterms, 1 final exam.

**Topics:** (Vector Spaces) - Subspaces, Intersection, Sum, and Direct Sum. (Finite Dimensional Vector Spaces) - Span, Linear Independence, Bases, and Dimension. (Linear Maps) - Null Space, Ranges, Rank, Matrices, and Invertibility. (Polynomials) - Degree, Real Coefficients, and Complex Coefficients. (Eigenvalues and Eigenvectors) - Invariant Subspaces, Upper Triangular Matrices, and Diagonal Matrices. (Inner Product Spaces) - Inner Products, Norms, Orthonormal Bases, Orthogonal Projections, Minimization Problem, Linear Functional, and Adjoints. (Operators on Inner Product Spaces) - Self Adjoint, Normal Operators, Spectral Theorem. (Operators on Complex Vector Spaces) - Generalized Eigenvectors, Characteristic Polynomial, Minimal Polynomial, and Jordan Form.

**Textbooks:** Linear Algebra Done Right by Sheldon Axler (Good)

**Study-aides:** N/A

**Comments:** Since this is a proof-based class, you need to know all the definitions and theorems by heart. That way, when you are taking the exam, you can quickly jot down all the relevant information to a problem/proof to help you formulate an answer. The best way to learn the material is by explaining to other people in your own words the importance of a theorem, etc. For the weekly problem set, work together with a group of people, that way if you can discuss your approach to the problems and get feedback.
“110 will lay foundations for all of the physics you will ever do.”

**About 113: ** Offered every semester in the school year, and during the summer.
“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.”

**About 121A: Mathematical Tools for the Physical Sciences ** Offered every semester in the school year, and during the summer.

**About 121B: ** Offered every semester in the school year, and during the summer.

**Prerequisites:**Math 53, Math 54

**Format:** 4 units; 3 hour lecture per week; 1 hour discussion; Problem set due each week + occasional programming assignments and quizzes.

**Grading:**B average, 1-2 in-class midterms, 1 final exam.

**Topics:**Preliminaries and error analysis (round-off errors, computer arithmetic, algorithms and convergence), solutions of equations in one variable (bisection method, fixed-point iteration, Newton's method, accelerating convergence, zeros of polynomials, Muller's method), Interpolation and polynomial approximation (Lagrange polynomial, Neville's method, divided differences, hermite interpolation, cubic spline interpolation), Numerical differentiation (richardson's extrapolation), Numerical integration (composite integration, Romberg integration, adaptive quadrature methods, gaussian quadrature), Initial value problems for ordinary differential equations (theory, Euler's method, higher-order Taylor methods, Runge-Kutta methods, Runge-Kutta-Fehlberg methods, multistep methods, higher-order equations, systems of differential equations, stability, stiff differential equations), Linear systems (pivoting strategies, linear algebra, matrix inversion, determinant of matrix, matrix factorization)

**Textbooks:** Numerical Analysis - Burden and Faires

**Study-aides:** Notes and sample code (http://persson.berkeley.edu/128A/), past exams (https://tbp.berkeley.edu/students/exams/math/128A/)

**Comments:** N/A

**About 128B: ** Offered every semester in the school year, and during the summer.

**About 185: ** Offered every semester in the school year, and during the summer.
“Stuff you learn in 185 is useful in surprising situations.”
“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

**Prerequisites:**None!

**Format:**4 units; 3 hr lecture, 1 hr discussion. Problem set each week

**Grading:**B+ average, 2 in-class midterms, 1 final exam, lab activities.

**Topics:**This course is for non astronomy/physics physical science majors to explore astronomy and to also fullfill the physical science breadth. If a student takes 7A or 7B he/she will not get any credit for this course. Topics include structure and evolution of stars, galaxies, and the universe, quasars, pulsars, black holes, extraterrestrial communication.

**Textbooks:** The Cosmos, 4th Edition, Pasachoff

**Study-aides:** N/A

**Comments:** Lecture is webcasted for convenience and because the course is overenrolled (800 students for a 700-person auditorium).
“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.”
“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.” - Jonathon Li, undergraduate applied math

**Prerequisites:** Physics 5ABC and 5BL,5CL or 7AB and Math 1A and 1B or equivalent

**Format:** 4 units; 3 hr lecture and 1 hr lab

**Grading:**B average, homework, exam

**Topics:** Offered only in Fall. This is the first part of an overview of astrophysics, with an emphasis on the way in which physics is applied to astronomy. This course deals with the solar system and stars, while 7B covers galaxies and cosmology. Solar system topics include orbital mechanics, geology of terrestrial planets, planetary atmospheres, and the formation of the solar system. The study of stars will treat determination of observations, properties and stellar structure, and evolution. The physics in this course includes mechanics and gravitation; kinetic theory of gases; properties of radiation and radiative energy transport; quantum mechanics of photons, atoms, and electrons; and magnetic fields.

**Textbooks:**Caroll, An Introduction to modern astrophysics 2nd edition

**Study-aides:**

**Comments:** “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 math and astrophysics alumnus
“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.”

**Prerequisites:** Physics 5ABC,5BL,5CL or 7ABC and Math 1A,1B or equivalent

**Format:** 4 units; 3 hr lecture,1 hr lab

**Grading:**B+ average, homework, exam

**Topics:** Offered only in Spring. This is the second part of an overview of astrophysics, which begins with 7A. This course covers the Milky Way galaxy, star formation and the interstellar medium, galaxies, black holes, quasars, dark matter, the expansion of the universe and its large-scale structure, and cosmology and the Big Bang. The physics in this course includes that used in 7A(mechanics and gravitation; kinetic theory of gases; properties of radiation and radiative energy transport; quantum mechanics of photons, atoms, and electrons; and magnetic fields) and adds the special and general theories of relativity.

**Textbooks:**

**Study-aides:**

**Comments:** “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

**Prerequisites:** Physics 110A, Physics 110B or Physics 137A, Physics 137B, (Physics 112), Astro 7A, Physics 7C

**Format:** 4 units; 3 hr lecture, 1 hr discussion. Problem set each week

**Grading:**B average, 1-2 midterms, final, homework, programming assignments (depends on professor).

**Topics:** Review of basic astrophysics (Blackbody radiation, flux, magnitudes, Boltzmann equation, Saha equation, HR diagrams). Stellar formation (Hydrostatic equilibrium, Virial theorem, Jeans criterion, Free-fall time). Radiative transfer (Opacity, Optical depth, radiative transfer equation, Local Thermodynamic Equilibrium). Stellar atmospheres (Absorption & Emission lines, Broadenings). Stellar modelling(Equations of stellar structure, Energy transports, Polytropes & Lane-Emden equation). Nucleosynthesis. Degenerate stars(White dwarfs Chandrasekhar limit, Gamow peak, Black holes, Schwartzschild metric)

**Textbooks:** Leblanc - Stellar Astrophysics (moderate).

**Study-aides:** Professor Quataert's site (Fall 2011): http://astro.berkeley.edu/~eliot/Astro160/160.html
Professor Marcy's site (Fall 2013): http://astro.berkeley.edu/~gmarcy/astro160/

**Comments:** “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 and astrophysics alumnus

**Prerequisites:** Physics 110A and Physics 110B, Physics 112(concurrent)

**Format:** 4 units; 3 hr lecture, 1 hr discussion. Problem set each week

**Grading:**B+ average, 1-2 midterms, final, homework

**Topics:** Offered only in Spring. Elements of general relativity. Physics of pulsars, cosmic rays, black holes. The cosmological distance scale, elementary cosmological models, properties of galaxies and quasars. The mass density and age of the universe. Evidence for dark maater and dark energy and concepts of the early universe and of galaxy formation. Reflections on astrophysics as a probe of the extrema of physics.

**Textbooks:** Ryden, Introduction to cosmology

**Study-aides:**

**Comments:** N/A

**Prerequisites:** Physics 5ABC or 7ABC and Math 53, Math 54 or Physics 89

**Format:** 4 units; 3 hr lecture

**Grading:**B+ average, presentations, homework, (final exam)

**Topics:** Offered only in Fall. Physics of planetary systems, both solar and extra-solar. Star and planet formation, radioactive dating, small-body dynamics and interaction of radiation with matter, tides, planetary interiors, atmospheres and magnetospheres. High-quality oral presentations required.

**Textbooks:** Lissauer, Fundamental Planetary Science: Physics, Chemistry and habitability

**Study-aides:**

**Comments:** “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. Apparently Courtney Dressing will be teaching this course in the future so she may have different exam schedule.”-Andrew Hsu

**Prerequisites:** Physics 5ABC or 7ABC and Math 54 or Physics 89

**Format:** 4 units; 4 hr laboratory 1 hr lecture

**Grading:**B+ average, 4-6 experiments

**Topics:** Offered only in Fall. This course requires four to six experiments such as: accurate position and brightness measurements of stars; laboratory exploration of the characteristics of two-dimensioonal charge-coupled devices and infrared detectors; measurement of the distance, reddening, and age of a star cluster; measurement of the Stokes parameters and linear polarization of diffuse synchrotron and reflection nebulae; measurement of the period and pulse shape of the Crab pulsar using Fourier techniques. Professional telescopes will be used such as those at Leuschner and Lick Observatory. There is an emphasis on error analysis, software development in the IDL language, and high-quality written reports.

**Textbooks:** None

**Study-aides:**

**Comments:** “Be aware that if you are not a senior you are very unlikely to even be able to enroll in this Optical Lab course because priority is given to seniors who are graduating within a year. As a non-senior you will be competing against like 20 other non-senior for one last spot (that a senior gave up) in the class.”-Andrew Hsu

**Prerequisites:** Physics 5ABC or 7ABC and Math 53, Math 54 or Physics 89 and Astro 7A-7B, Physics 110B recommended

**Format:** 4 units; 4 hr discussion 1 hr lecture

**Grading:**A- average, lab reports

**Topics:** Offered only in Spring. Several basic laboratory experiments that concentrate on microwave electronics and techniques; construction of receiving, observing, and data analysis systems for two radoastronomical telescopes, a single-dish 21-cm line system and a 12-GHz interferometer; use of these telescopes for astronomical observing projects including structure of the Milky Way galaxy, precise position measurement of several radio sources, and measurement of the radio brightness distributions of the sun and moon with high angular resolution. There is a heavy emphasis on digital data acquisition, software development in the IDL language, and high-quality written reports.

**Textbooks:** None

**Study-aides:**

**Comments:** “Be aware that if you are not a senior you are very unlikely to even be able to enroll in this Radio Lab course because priority is given to seniors who are graduating within a year. As a non-senior you will be competing against like 20 other non-senior for one last spot (that a senior gave up) in the class.”-Andrew Hsu
Offered spring semesters.
“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