# Is this mathematics course choice OK?

1. Apr 25, 2015

### Blue and green

I'm starting college soon.

2015
Summer
Calculus I and Analytic Geometry
Pre-calculus and Analytic Geometry

Fall
Calculus II and Analytic Geometry
Calculus I for Life Sciences
Linear Algebra
United States History I
United States History II

2016

Spring
Calculus III and Analytic Geometry
Calculus II for Life Sciences
Discrete Mathematics
Differential Equations
Symbolic Logic

Summer
Introduction to Computer Programming
General Physics I

Fall
Analysis I
Complex Analysis I
Honors Linear Algebra
Abstract Algebra
Numerical Analysis

2017

Spring
Analysis II
Classical Geometries
Introduction to Topology
Introduction to Theory of Sets
Ordinary Differential Equations

Summer
General Physics II

Fall
Combinatronics
Cryptography
Introduction to Topology II
Honors Complex Analysis
Groups, Rings, and Fields

2018

Spring
Ring Theory
Differentiable Manifolds
Algebraic Topology
Theory of Sets
Riemannian Geometry

Summer
Data Structures
General Physics III

2. Apr 25, 2015

### micromass

Why would you take Calculus I and II multiple times??
And taking calculus over the summer really isn't a very good idea.

3. Apr 25, 2015

### axmls

Also, calculus and pre-calculus in the same semester?

4. Apr 25, 2015

### micromass

Also, you take Linear Algebra and Honors linear algebra (and the same with complex analysis). Just take the honors version immediately.

You'll likely need analysis for complex analysis

You will need differentiable manifolds for Riemannian geometry.

5. Apr 25, 2015

### Niflheim

This looks kind of like a random list of math courses.

6. Apr 25, 2015

### Loststudent22

What university are you going to? They generally have a typical road map laid out on what you need to take. The courses you listed right now don't make a lot of sense.

7. Apr 26, 2015

### QuantumCurt

You're taking pre-calculus and calculus I at the same time? This isn't really how things work.

You're also suggesting that you would also take calculus for the life sciences I and II, in addition to calculus I and II. This is pointless. These classes are going to cover the exact same material, but the life science variant is going to focus more on applications and less on theory or rigor. You're likely thinking that the wider exposure will be a good thing...but trust me, there is no point at all for you to take calculus for the life sciences. It's an abridged calculus for people that don't necessarily like math or really need that much of it for their career.

You have several instances of courses within the same semester as their typical prerequisite courses, which really isn't going to work out. You'll likely need linear algebra prior to abstract algebra, and real analysis prior to complex analysis. I see general physics I in the summer, and general physics II the following summer. I would strongly advise against this. Physics are the types of classes that you want to spend some time with. You don't want to cram them in during the summer, and you really want to take them back to back. Having a year between the two would make the second semester a bit harder.

This really does read like just a list of math classes. You have US History I and II mixed in there, and during the same semester. You may not be able to take them concurrently, although a prerequisite in a history class is often more of a formality. What about the rest of your general education courses? Are you bringing in a ton of AP credit and eliminating most of your GenEd courses?

8. May 19, 2015

### Blue and green

I've taken out the Calculus for Life Sciences realized I needed to take a foreign language. I've taken some writing courses and also Elementary Statistics, covering my general education requirements. Re Physics in the summer I learn quickly so I'm not worried. The units per summer session of those quantitative courses are within limit so reasonable study time is expected, and likely - should be, after all.

9. May 19, 2015

### Blue and green

Also, replaced one of those calc. life science courses with Physics I, and also moved up the computer programming course.

10. May 19, 2015

### micromass

That's the high school experience talking. Once you go to an actual college, things are very different. There are many people who breezed through high school and who struggled very much in their first college year. Don't be one of those, so don't underestimate college.

First of all, it is worth knowing physics well. And taking a quick summer course and learning quickly means you might be able to do well on the exams. But it won't necessarily mean you have a solid knowledge of physics. You need time for physics, and if you rush it over the summer, chances are big you won't have the indepth knowledge you need.

11. May 19, 2015

### Staff: Mentor

I strongly suggest that you take General Physics I-III during consecutive semesters. Stretching them out one course per summer means that you're going to forget a lot of stuff during the years in between. Physics is hard enough as a summer course to begin with. Summer terms are shorter with more class hours per week, right? I used to teach general physics in summer school and always thought of it (to myself) as "firehose physics."

12. May 19, 2015

### SteamKing

Staff Emeritus
I'm not sure what "Combinatronics" is. Is that where you grab a box of random electronic parts and try to make a working gizmo?

Out of this grab bag of courses, it's not clear what your goal is in going to college. What sort of degree do you hope to obtain? What is your major field of study?

13. May 19, 2015

### Blue and green

B.A. in Mathematics, then Ph.D in mathematics.

14. May 19, 2015

### Blue and green

How easy would admission to Princeton or UC Berkeley be from doing this course alone, and the GRE with recommendations, from UC Berkeley or UCLA?

15. May 19, 2015

### Blue and green

For doctoral program in mathematics, specifically analysis.

16. May 19, 2015

### micromass

Admission to Princeton or Berkeley is never easy.

17. May 20, 2015

### esuna

This is a rough outline of a more feasible version of your schedule... It doesn't hit everything you wanted, but it would be a solid degree without you jumping off the roof of your dorm complex.

2015
Summer
Pre-calculus and Analytic Geometry

Fall
Calculus I and Analytic Geometry
United States History I
Introduction to Computer Programming
Symbolic Logic

2016

Spring
Calculus II and Analytic Geometry
General Physics I
United States History II

Summer
(find something)

Fall
Calculus III and Analytic Geometry
Honors Linear Algebra
General Physics II
Discrete Mathematics

2017

Spring
General Physics III
Combinatorics
Differential Equations
Analysis I

Summer
(find something)

Fall
Abstract Algebra
Analysis II
Differentiable Manifolds

2018

Spring
Introduction to Topology I
Abstract Algebra II
Riemannian Geometry

Summer
(something)

18. May 20, 2015

### Blue and green

Can not do that. In fact, I'm interested in slightly exceeding university credit limits upon transfer.

19. May 22, 2015

### Blue and green

Can't do Calculus after the summer if I want to transfer on time.

20. May 22, 2015

### Blue and green

(which I do)
- Blue

21. May 22, 2015

Seriously your schedule has things like Calc 2 for life sciences at the same time as Calc 3. Gen Physics 3 (Calc 1-2) after Real Analysis and Topology. Is this a joke?

22. May 23, 2015

### QuantumCurt

"Some writing courses and also Elementary Statistics" typically isn't enough to cover all of your Gen Ed requirements. Typical Gen Ed requirements include two semesters of social sciences, two semesters of humanities and fine arts, a couple of English composition courses, a communications/speech type course, and a third or fourth level of a language. Will you have all of these requirements met?

How fast you learn is beside the point. It is a bad idea to take physics in the summer, and it is a bad idea to have an entire year between your physics courses. Physics takes time. It isn't like cramming a humanities course into the summer. It's not just a matter of it being more difficult in the summer. It's also the fact that you almost definitely will not learn as much physics while taking it in the summer. In principle it will cover the same material. But things like defined formulas are more likely to just be taken for granted, rather than developing them and seeing the why and the how of the defined formulas.

There's really no answer to this question, and at the point you are currently at in your education it's a pointless question to even ask. Admission to Princeton or UC Berkeley is never going to be easy. Someone could take all of these courses and ace every single one of them. Such a student -could- have a good shot at either school. Someone could take all of these courses and do mediocre in all of them. Such a student would not have as good of a shot at these schools. Research and overall involvement in the field play just as big of a part in it as the range of courses you've taken.

You say that you can't take calculus after the summer if you want to graduate on time. Obviously everyone wants to graduate on time, but there is a course called "pre-calculus" for a reason. It teaches you the material that you need to know to be prepared for calculus. I highly doubt that you'll be able to take pre-calculus and calculus I at the same time.

You're counting your chickens before your eggs have hatched. You're asking about your chances for getting into a mathematics PhD program at some of the most prestigious schools in the country when you haven't even started calculus yet. Take things slow. Remember that you have ~4 years of college left. Thinking ahead is very good, but thinking too far ahead is pointless. I can almost guarantee you that any course sequence you come up with now will not work out as far as timing and logistics are concerned. You will almost certainly encounter instances of classes overlapping one another, and going by the list you laid out, you will -definitely- encounter numerous prerequisite issues.

Last edited: May 23, 2015
23. May 23, 2015

### micromass

I'm sorry, but I find this hard to believe. Can you be more specific? Why do you think you won't be able to transfer on time?

24. May 23, 2015

### micromass

I agree with your entire post. But precalculus is very often a quite useless course. If one knows trigonometry and a bit of geometry, then they should be able to handle calculus perfectly. Many students do skip the precalculus course and do fine. It seems like it's more of a "mathematical maturity" thing.

Of course, if the university put precalculus as a formal prerequisite, then chances are big that you can't get around it.

25. May 23, 2015

### QuantumCurt

This is quite true. I never took a formal precalculus class and I've done very well in all of my math classes. However, I took separate college algebra and trigonometry classes. Precalc is really nothing more than a combination of these topics. Has OP taken any college algebra or trig? If not, then precalc is a mandatory prerequisite that can't and shouldn't be avoided. Going into calculus without any background in trig is not going to be a good time.