Class of 2020 Blog

Posts from the Johns Hopkins Class of 2020

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Guide to Intro Math and Physics

If there’s one thing that Hopkins certainly doesn’t lack, it’s introductory Math and Physics courses. There are multiple levels of every class from Calculus I to Differential Equations, some focused on biology applications, some on engineering, and some Honors level courses where you dive deep into the pure math.

And math has nothing on physics: there are four levels to General Physics I & II. Yes, four entirely separate tracks for learning classical Mechanics and Electromagnetism.

Seeing entire pages of just introductory physics on SIS can be a bit daunting, so I hope this guide can help choose the best class for you.

yes, this is just calc I and II

yes, this is just calc I and II


Physics

There are four levels of general physics:

  • (AS.171.101-102) General Physics I & II for Physical Science Majors
  • (AS.171.103-104) General Physics I & II for Biological Science Majors
  • (AS.171.107-108) General Physics I & II for Physical Science Majors Active Learning
  • (AS.171.105-106) Classical Mechanics I & Electricity and Magnetism I

Obviously, based just on the names, one can guess that the target group is a bit different for each class.

AS.171.101-102 and 107-108 are targeted to pretty much everyone who isn’t a Biology/BME/ChemBE major (or any of the other 100 biology-infused majors we seem to have at Hopkins) or a Physics major. These classes are going to cover your standard general physics content, from kinematics and Newton’s laws to basic orbital mechanics and mechanical waves in the first semester, and from electrostatics to optics in the second. 107-108 is the active learning variant, where information is presented via guided problem solving rather than your typical lecture style.

AS.171.103-104 are targeted to anyone majoring in a biological science. You’ll still have a rather standard physics curriculum, but with an infusion of biology applications, e.g. discussing fluid dynamics’ application to the flow of blood in the circulatory system.

AS.171-105-106 are designed especially for physics majors. We dive deeper into the content, and as is standard in physics departments worldwide, jokes about biology and engineering being inferior will be made weekly. Since we have entire courses on Thermodynamics, Optics, etc., we focus more on the fundamentals. For example, we didn’t touch the topic of fluid dynamics in Classical Mechanics last fall, but the other general physics courses certainly did.

Another option for physics majors who scored a 4/5 on both AP Physics C exams is to skip the first year of physics altogether, and go straight to Special Relativity. I really wouldn’t recommend this unless you had a world-class physics education in high school. If your high school physics taught in detail how to solve mechanics problems using the theory around first and second order differential equations, vector calculus, and basic wave mechanics, then I’d consider this. However, getting a taste for Hopkins-level physics before diving into Einstein’s theory is probably a good idea.

What class should I take?

Physics

intro physics flow chart

pdf link


Mathematics

There are many courses in the intro math track:

  • (AS.110.105) Introduction to Calculus
  • (AS.110.106-107) Calculus I/II for Biological and Social Sciences
  • (AS.110.108-109) Calculus I/II for Physical Sciences and Engineering
  • (AS.110.113) Honors One Variable Calculus
  • (AS.110.201) Linear Algebra
  • (AS.110.212) Honors Linear Algebra
  • (AS.110.202) Calculus III
  • (AS.110.211) Honors Multivariable Calculus
  • (AS.110.302) Differential Equations

Introduction to Calculus reviews topics generally covered in high school Algebra II and/or Pre-Calculus classes. If you’re not confident in your knowledge of algebra, trigonometry, logarithms, and functions, this course will sure up the foundation before you start calculus.

Calculus I/II for Biological and Social Sciences are targeted to biology and social science majors. Since many students in these majors are unlikely to take more than 3 or 4 semesters of math, this track is a bit more all-encompassing, and will give a basic level understanding for a broader reach of subjects. Additionally, applications to bio/social sciences will be covered, e.g. probability topics in clinical trials.

Calculus I/II for Physical Sciences and Engineering are the “default” calculus courses. They cover everything in the standard single variable calculus curriculum: limits, derivatives, integrals, and Taylor series.

Honors One Variable Calculus is intended for students with a strong ability in math, who want to learn single variable calculus in a more theoretical complex. While not proof-based like, say, Honors Linear Algebra, proofs will be presented. If you hated those 10 minutes your teacher might have spent talking about the delta-epsilon formal definition of a limit, then this class is not for you, as you will spend hours calculating limits using this rigorous process.

Linear Algebra is all about the theory behind vectors and matrices. It’s highly applicable to computer science and programming, but also serves as a basis (pun intended) for Vector Calculus and Differential Equations.

Honors Linear Algebra covers everything regular Linear Algebra does, but delves further into the theorems and proofs underlying the algorithms and methods you learn in regular LinAlg. This is the first proof-based course that most math majors take, so it’s a good training course for the advanced proofs you see in Advanced Algebra, Real Analysis, and other 400 level mathematics courses.

Calculus III consists of extending everything you learned in Calculus I to 3-dimensional space. Since we live in 3 spatial dimensions, this is obviously very important for pretty much every single major that deals with modelling the real world, from Comp. Sci. to MechE to Physics.

Honors Multivariable Calculus is (was?) a course that approaches Calc III topics more theoretically. I took this course last fall, and while it was incredibly interesting, I found that generalizing to n-dimensional space and learning everything from this general sense took away time from really nailing down my 3-dimensional knowledge. I heard speculation that the math department was no longer going to offer the course, in part for this reason. I suppose that is indeed what they chose to do, seeing as HMVC is not offered in Fall 2017. I wouldn’t recommend taking this course unless you have already taken a vector calculus course in high school or at a local community college.

Differential Equations is all about solving problems where you only know how some variable is changing. Heat moving through a steel rod or a swinging pendulum are examples of this. This class, while a 300 level course, definitely “feels” more like Calc BC/Calc II, where you’re just learning a bunch of methods to solve various different integrals. In DiffEq, you learn how to diagnose what type of ordinary differential equation a given ODE is, and then using a method suited for that type. Much of the material, especially later on in the course, builds on concepts learned in LinAlg and Calc III, so I’d recommend taking them before or at least concurrently with DiffEq.

What class should I take?

intro mathematics sequence flow chart

intro mathematics sequence flow chart

pdf link


Doubling Up

Theoretically, LinAlg, Calc III, and DiffEq can all be taken in any order. However, I wouldn’t suggest all pairings:

Very doable:

  • LinAlg and DiffEq. DiffEq uses a lot of matrices in the latter half of the course, but you learn many methods to solve problems using matrices before or at the same time in LinAlg.

Doable:

  • LinAlg and Calc III. Calc III uses matrices, but in a limited capacity. Having already completed LinAlg will help you make more connections early on in Calc III, but it’s not 100% necessary.

Not recommended:

  • Calc III and DiffEq. Systems of differential equations use very similar math as vector calculus, e.g. the Jacobian, the Wronskian, etc. DiffEq moves quickly through these, so it might be difficult if it’s your first time seeing them. Calc III gives a good foundation for these chapters of DiffEq.

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