# [APMA 2101] Introduction to Applied Mathematics

- Departments: Applied Physics and Applied Mathematics
- Professors: David Keyes, Marc Spiegelman, and Michael Tippett

Professor Tippett is very helpful in class and in office hours. In general, he is a great teacher.

The class size was huge (In the big room in Havemeyer) and the professor could not be heard well from everywhere. He used good examples in class which clarified my concepts a lot.

The homeworks were generally easy, and mainly from the book. The homeworks are graded by different TAs every week to make sure no one student keeps facing a harsh grader.

Midterms are often lengthy and include a good mix of easy, medium and hard questions. Midterms are usually out of 130-140 points, so losing a few points affects the percentage less than you would imagine. He also has bonus questions in all exams but they are usually much harder. Partial points are awarded. A solid understanding of the material is required to do well on the course.

I disagree with the previous comment regarding the curve. In the beginning of the semester he hands out an info sheet detailing the rough grade boundaries. (90+ A range,80+ B range etc) According to that I expected an A- given my percentage of 92-93% but ended up getting an A. In my opinion, while the original boundaries may not be the friendliest, he tries to stick to the boundaries. I do not think he downcurves at all.

#### Workload:

hw, midterm1, midterm2 20% each. Final is 40%

Homeworks took me 2-4 hours to complete.

LECTURES: Boring, long, proof based. Hard to follow. Makes lots of mistakes in class but answers questions well.

HOMEWORK: Mostly from the textbook. Two problem sets made by the professor--more difficult than textbook problems. Textbook problems not very indicative of exam questions. Each one for me took ~4 hours

EXAMS: Two midterms one is ODE, second is Linear Algebra. Generally average is in the ~70% range. Linear Algebra is easier to study for since we had the problems he made for the psets. ODE is harder to study for since we only had overly easy textbook problems. Final is evenly distributed through topics--questions as vague and confusing as preceding quizzes.

CURVE: Wow. I wanna make it clear that this is an opinion since I have no idea what other people got. The curve for me was awful. Did average on the quizzes and well on the homeworks and for some reason ended up with a not so hot grade... Also, I know this isn't unheard of but it is quite rare for a professor to fail a student... right?

tl;dr: wasn't hell but I suggest you look for a different professor if you could

#### Workload:

Weekly pset (20%) (for me, that was about ~4 hrs per pset)

2 Midterms (20% each)

Final (40%)

He said he put more weight on your final if that was to your benefit.

Overall, pretty good! The course was an introduction to differential equations and linear algebra. I have to say (possibly naively, seeing as I only just finished freshman year) that this was a very useful class. Critical material showed up in three of my other classes. I strongly recommend taking this as early as you can.

For the first half of the semester, we covered first-order differential equations in their many forms. These are very useful and showed up in my calc, physics, and EE classes, even during freshman year. The second half covered linear algebra and second order differential equations. I think most people (me included) felt that the first half was not that bad, but the second half got pretty trippy.

The textbook is not good. Advanced Engineering Mathematics. It is not helpful at all. Something iconic that I remembered was that on the first homework, it asked us to distinguish whether certain equations were linear or nonlinear. The definition of a nonlinear equation was: "A nonlinear equation is one that is simply not linear." The definition of a linear equation wasn't given until the next chapter. It wasn't a very good definition either. And there was more stuff like that everywhere.

Some of the linear algebra stuff was pretty weird and confusing. Just about everybody had trouble with it. To worsen the situation, the most confusing parts weren't in the textbook. I learned from a classmate that the stuff people had trouble with was pulled straight from a textbook listed on courseworks as recommended. He also told me that this textbook explained it clearly. To make matters even worse, some of the TAs didn't understand this part and couldn't help with it.

Now, I am highlighting the negatives a lot. But this was a good course! We covered 1st order ODEs, linear algebra, and a little bit of 2nd order ODEs. 1st order ODEs took the most time. I think that Professor Tippett covered everything pretty well. The first few lectures of each major unit were a little confusing (the linear algebra one especially), but after you got the hang of it (the homeworks were helpful), it became a lot easier.

Professor Tippett is a very nice man. I had to reschedule a quiz because of a competition, and he was happy to help me do so. He's a very smiley guy, and I find him very funny, in a dry sort of way. He makes a lot of simple mistakes (like writing '+' instead of '-'), and he solves the questions (as in, he doesn't copy them from notes), so the errors get carried through. However, he invites people to correct him as soon as they see mistakes. And when they do, he apologizes and redoes the problem, continuing from where he messed up. He also takes questions well. If somebody asks about something they don't understand (even if it's from weeks back), he'll go over it on the board. I believe that he really does want students to learn. I do think that he teaches well. In my opinion, he is an exceptional professor.

Tl;dr:

Very useful class. Bad textbook. One unit was very confusing (and was the main unit on one of the quizzes). Very nice, smiley, and helpful professor.

#### Workload:

Not bad. One problem set each week, and they're pretty short.

40% Final Exam (cumulative, but weighted towards latest units)

40% Quizzes (3 were scheduled, but we only had two. I don't know how that was resolved.)

20% Homework (lowest dropped)

The problems on the quizzes and final were a lot like the homeworks. The ODE stuff was easier on the quizzes and tests than on the homework. The linear algebra stuff was about the same difficulty.

I took Prof. Tippett for APMA E2101 - Intro. to Applied Math. Never have I before had a professor so bad that I felt the need to write a review. At the beginning Prof. Tippett was a decent professor even though he was prone to making mistakes while doing examples in class. However, for the first part of the semester when he was teaching ODEs, it was decent, but once we got into the Linear Algebra part of the course, he was dreadful and probably one of the worst professors I have ever had the displeasure of being taught by.

If you have to do the class, AVOID Tippett! It is the most painful experience I have ever been through.

#### Workload:

A problem set a week, 2 midterms and a final.

In theory, this course is awesome. It gets you through Differential Equations and Linear Algebra in only a semester.

The reality is that while Marc Spiegelman is one of the nicest guys I've ever met, he's extremely scatterbrained. When proceeding through lecture, he VERY frequently steps a few steps back finds a mistake and restarts. He often goes on tangents that make the material unnecessarily complex.

That said, the course does use Gilbert Strang's Linear Algebra text as "backup"...the Strang lectures are awesome. Zill is pretty dense and sometimes misguided, but is probably a good life-long resource for many engineers.

First midterm was easy, second one was not...there was more theory than I had expected.

#### Workload:

Just right. Some of the problem sets are tedious and time consuming, but in comparison to real EE courses, they're not that bad. A little more work than the Calc1-4 problem sets.

Spring 2011 was the first semester there were classes held in Noco 501. Unfortunately, I found myself expending more effort trying to stay awake than learning the material. However, I don't think this is necessarily a reflection of Spiegelman's charisma. It's THAT ROOM. So temperate, lighting so warm, chairs so comfy...

I actually felt kind of bad for Spiegelman, because people were falling asleep left and right. I even heard him mutter once, 'asleep in the first row...'

#### Workload:

bring caffeine...that sometimes worked for me.

GREAT TEACHER! He's very witty, smart, fun, blahblahbalhblah. I really recommend meeting him outside office hours, he gives great advice! The material in the class isn't really bad at all, a bit of work and attention into it and you should be completely fine! I have to highlight that Spiegelman was just great. It's a mix of ODEs and Linear Algebra. I feel I learned a good amount of each necessary to do basic things... I don't know (and don't think) if I will really need DE or Linear Algebra in my career (and I hope I don't), so for now I want to say that you should take this class instead of ODEs and Linear Algebra separately.

The only problem I found with this class is the grading. There are 5 quizzes, and if you can do/understand the homeworks (even if you use cramster, WHICH WAS GREAT!), you will do well on at least 4 of them (since he drops one). Everyone tended to do well, so the mean was continuously high (like 8.5-9). In addition, since everyone got the answers from cramster in the homeworks (or from each other), the average for the hws was pretty much an almost perfect score in all of them. The first thing is that if you don't do well in one of these, IT WILL MOST LIKELY hurt your grade at the end (in order to do well, doing really well in these is a requisite). What I disliked the most is that because of this effect, since the variance in these quizzes and hws was so ridiculously small and the averages were so high, is that the final exam had a ridiculous amount of weight. I had almost perfect scores on all my quizzes and got perfect scores on all the hws, and I felt I understood the material very well (and still do). I had a pretty bad amount of finals and they were all right next to each other, giving me a really rough finals week. I ended up messing up and it hurt me really badly, when I have friends that only had 2-3 finals to study for and were able to just perform better... I don't know, eh, I'm just really disappointed that in the end there's so much weight on the final...

REGARDLESS of this thing I deem a problem, Spiegelman is just cool as heck.

#### Workload:

Almost weekly homeworks (most answers are on cramster).

First off, everything that has been said about Professor Spiegelman is true. He's a great professor who truly does care about his students. His lectures are good (although this was his first semester teaching this course so it was apparent he was getting his bearings) and he's great in office hours. Future sections of this course under him will only get better.

The class, on the other hand, leaves a bit to be desired. It essentially tries to cover both ODEs and the basics of Linear Algebra in one semester. While I feel like I've walked away with a working basic understanding of both, I also find myself left a bit wanting for more depth, which pretty much means I'd have to take both a semester of ODEs and a semester of Linear Algebra, which then renders this class a bit of a waste.

Ultimately, I think it would be best if the applied math department sat down and rethought the introductory curriculum. I think this class might be a result of some obscure ABET requirement. That's fine, but I think a yearlong two semester "Introduction to Linear Systems" core block that blended a thorough treatment of ODEs (including laplace transforms), Linear Algebra and an introduction to Linear Systems and discretization/numerics would be much more useful. (He tries to weave Matlab in a bit, but in a yearlong course, a lightweight lab could be thrown in...)

That said, if you're taking the class, you're probably in SEAS, which means you have to.

To sum up Spiegelman, on the last day of class he said: "If you ever have any questions about material related to the material in this course, come see me! I'll be here, they gave me tenure hehehe.." Really, that's about the best you can ever ask for from a professor.

#### Workload:

Quasi weekly problem sets of varying difficulty. 6 20 minute quizzes in lieu of midterms. Fairly difficult final (open book/notes/anything-on-paper, although I found that I was reluctant to pull the book out during the final, even to my own detriment).

Brilliant Professor teaching an introductory class. He cares about his students - use him and his TAs as resources and you will do well. Relatively generous end of semester curve. Lazy BMEs might struggle.

#### Workload:

Medium - hard to study for the quizzes and problem sets are worth a lot (very worth the effort). No midterm - final is difficult.

Simpley put, David Keyes is way too smart for this class. He's brilliant. I think that the teaching of the class is just too smart for the class.

The concepts are hard (especially ODEs) and the exams and quizzes are worded really differently from the homework, so it makes them really challenging. But judging by if you're reading this review, 2102 isn't a choice for you. You have to take it, and Keyes is the only instructor.

#### Workload:

8 Problem Sets (All nighters the night before they were due), 6-7 hard quizzes, 1 ridiculous exam. It's a hard class.

I think both reviews of Dr. Keyes are fair. Dr. Keyes clearly loves teaching, and will send you multiple witty and informative emails every day. If you feel lost in lecture, don't feel too bad. He lectures at a very high level and loses most of the class mid way through lecture, I think. The textbook was not bad, although I used an older version. I recommend supplementing your notes with Wikipedia articles, which are extremely clear and provide good examples.

One thing you need to get used to quickly--Dr. Keyes writes a lot on the board AND on the quizzes. Quiz questions are often paragraphs in length. And the questions are not always straightforward, they require some ingenuity. Do not let the length of the question scare you. Partial credit was always generous.

The final exam was quite difficult this year, and he told us in an e-mail that the previous year was too easy, and this year was too hard. So next year will probably be a compromise, but do prepare to be tested on some of the most obscure parts of the course.

I found Keyes to be both supportive and so accessible. He travels a lot, and despite this, answered many of my questions at late hours via e-mail. And he's psyched about math, so enjoy him.

#### Workload:

6 quizzes, drop 1. An EXTRA quiz is given during reading week, so take that and it's 7 quizzes, drop 2. Biweekly problem sets that get progressively longer as the semester goes on. Open book/note final that you will need to study for.

Professor Keyes definitely knows the material and is actually exited about it, but he does not teach the class in a straightforward, clear-cut way. Especially for an introductory class youÂ’d expect the concepts to be laid out logically and with patience, but this is exactly what Prof. Keyes does not do. His handwriting is very legible on the board, but he writes too much too quickly and skips over a good portion of the material. Instead, he fills class time explaining special cases and other things not directly related to the book material or homework. The only way to easily follow what heÂ’s doing in class is to read the book material beforehand and understand it. Unfortunately the book (Â“Advanced Engineering MathematicsÂ”, used Spring Â’06 semester) is also a problem because it is longwinded and hard to follow. One of the common problems in the book is that it only explains techniques once, often inadequately. Sample problems can be hard to understand because the book doesnÂ’t take the time to write out a full explanation, skipping over parts from previous sections it assumes you know perfectly well. For this reason doing the homeworks (homeworks consist of book problems) can feel like a logic game; I spent a lot of time just figuring out how the book did the sample problems! The TAÂ’s arenÂ’t that great, so donÂ’t expect to get much from recitation. Overall however, the class could be a lot worse, and especially if youÂ’re familiar with the material it doesnÂ’t take too much effort to walk away with a decent grade.

#### Workload:

Homeworks consist of book problems and are due every one or two weeks. They are slightly too long. There are quizzes every few weeks which are difficult because they do not always correlate with the homeworks/book material. There is no midterm. One homework and one quiz are dropped.

Professor Keyes is one of the best math teachers I've ever had. He loves teaching and tries his best to present very dry topics with some level of engagement. He is really, really dorky but he can be funny that way. He's very accomodating with scheduling quizzes and problem sets for religious holidays and such.

He'll sometimes lose most of the class during lecture, but the material he covers is usually above what you need to know for the quizzes.

He does one of the three weekly recitations himself, in which he'll give you a good idea of what's going to be on the next quiz (as opposed to the TAs, who seemed pretty incompetent as teachers).

AMPA 2101 is probably a class you'll have to take. It's not such a killer.

#### Workload:

Eight reasonable problem sets, six in-class quizzes, and a final. One bonus problem set and final to make up for one for an equivalent to dropping two quizzes.

## Directory Data

Dept/Subj | Directory Course | Professor | Year | Semester | Time | Section |
---|---|---|---|---|---|---|

APAM / APMA | APAM APMA E2101: Intro to Applied Mathematics | Marc Spiegelman | 2013 | Spring | TR / 1:10- 2:25 PM | 1 |

APAM / APMA | APAM APMA E2101: Intro to Applied Mathematics | Marc Spiegelman | 2012 | Spring | TR / 1:10- 2:25 PM | 1 |

APAM / APMA | APAM APMA E2101: Intro to Applied Mathematics | Marc Spiegelman | 2011 | Spring | TR / 1:10- 2:25 PM | 1 |

APAM / APMA | APAM APMA E2101: Intro to Applied Mathematics | Marc Spiegelman | 2010 | Spring | TR / 1:10- 2:25 PM | 1 |

APAM / APMA | APAM APMA E2101: Intro to Applied Mathematics | David Keyes | 2009 | Spring | TR / 1:10- 2:25 PM | 1 |

APAM / APMA | APAM APMA E2101: Intro to Applied Mathematics | David Keyes | 2005 | Spring | TR / 1:10- 2:25 PM | 1 |

APAM / APMA | APAM APMA E2101: Intro to Applied Mathematics | David Keyes | 2004 | Spring | TR / 1:10- 2:25 PM | 1 |