Is this mathematics course choice OK?

[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
Advanced Computer Programming
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

 

[micromass]

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

 

[axmls]

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

 

[micromass]

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

Analysis I
Complex Analysis I

You'll likely need analysis for complex analysis

Differentiable Manifolds
Algebraic Topology
Theory of Sets
Riemannian Geometry

You will need differentiable manifolds for Riemannian geometry.

 

[Niflheim]

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

 

[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.

 

[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?

 

[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.

 

[Blue and green]

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

 

[micromass]

Re Physics in the summer I learn quickly so I'm not worried.

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.

 

[jtbell]

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."

 

[SteamKing]

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?

 

[Blue and green]

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

 

[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?

 

[Blue and green]

For doctoral program in mathematics, specifically analysis.

 

[micromass]

Admission to Princeton or Berkeley is never easy.

 

[heatengine516]

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 Logic2016

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

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 ISummer
(find something)Fall
Abstract Algebra
Analysis II
Differentiable Manifolds

2018

Spring
Introduction to Topology I
Abstract Algebra II
Riemannian GeometrySummer
(something)

 

[Blue and green]

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

 

[Blue and green]

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

 

[Blue and green]

(which I do)
- Blue

 

[crador]

Your courses are backwards. Take the math courses in order and fill blanks with science to support. Ask an academic advisor at your chosen institution for help.

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?

 

[QuantumCurt]

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.

"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.

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?

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.

 

[micromass]

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

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?

 

[micromass]

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 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.

 

[QuantumCurt]

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.

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.

 

[Blue and green]

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?

I'm transferring after "one year" of my formal course.

 

[micromass]

I'm transferring after "one year" of my formal course.

I don't really get it. Why would not taking calculus over the summer not allow you to transfer after one year?

 

[QuantumCurt]

I don't get it either.

It might help if you explain a bit more about your specific situation. Are you attending a community college and then transferring to a university after a year?

If this is the case, you'll be transferring as a sophomore. In the majority of cases, one will not be required to have previously completed the entire calculus sequence as a sophomore transfer. A junior transfer would be required to have completed the whole calculus sequence.

If not having calculus 3 would prevent you from transferring to your target school after one year, then you may have to simply accept it. You keep saying that it will only work if you take calculus in the summer, but it may simply not be possible. It would be highly unusual for a school to allow one to take calculus at the same time as precalculus. You need to discuss this with an adviser at your school, and an adviser at the school to which you intend to transfer.

I've asked already, but what level of mathematics have you completed? Have you completed courses in college algebra and trigonometry? These two courses are precalculus. If you've taken them, it's quite possible that you won't even need precalculus. This would solve the problem. I still wouldn't suggest taking calculus I in the summer, but you sound set on that. However, this is the only exception to a precalculus prerequisite that I can think of.

 

[one]

My advice to OP is to not worry about planning out your entire curriculum. It is a good idea to know your degree requirements and how you intend to complete them, but what you want to/need to take will likely change after every semester.
I remember I did the same thing before I started college, listing out the courses I wanted take each semester. What I actually decided to take looks almost nothing like what I planned :)

Good luck. I second the recommendation that you should talk to an academic adviser, if you can, so that they can better address your specific situation.