Is an Intro to Logic Class Helpful for Transitioning into Higher Mathematics?

[TheKracken]

Alright, so I will be registering for classes at my community college here in a few days and I am having a hard time deciding on classes. I am hoping to major in mathematics or physics (leaning toward pure math) and I hope to transfer to UC Berkeley (I have a 3.7 first semester)

Some of the options I have for classes next semester for my GE class other than German are:

Micro Economics (taking Macro right now, I like it a bit)
Art History renaissance (taking the pre history one right now and enjoy it a bit.)
INTRO TO LOGIC---This class is in the philosophy department and does not seem to be math based but would this help me with transitioning into higher mathematics and proof courses? Here is the class description:
PHIL 208 - Intro To Logic
Presents a study of language and its functions, definitions, informal fallacies, inductive reasoning, and concepts and techniques of logic. Advisory: Eligibility for ENGL 156. Transfer: CSU; UC. (Formerly PHIL8)

If anyone could please help me decide. I am going to be in pre calculus next semester (taking trigonometry right now) and I hope that this class could give me some sort of insight into mathematics.

 

[R136a1]

Do you know the book the class will use? Or do you have some previous homework/exams? That would make it easier to judge.

What other options do you have for classes?

I'm really not against a basic logic class, even if it's not very mathy. It is a subject that deserves some study if you're into math, even the informal logics.

 

[MarneMath]

I think any course that forces you to learn deductive and inductive argument is valuable for anyone looking to major in math or science. The ability to critically think about arguments and the world around you is an acquired skill and the more you practice it the better off you'll be. For me personally, the only general elective that I felt truly benefit me in my field was a non-math logic course, because it forces you to break down every argument include the unstated conclusions that we often gloss over. More over, you will probably cover deductive arguments and therefore learn modus ponens and modus tollens which is something you'll see over and over again in mathematics :).

 

[Student100]

Kracken, have you given up on BioPhysics or the other Majors you thought about pursuing? You should try to decide on what you want to transfer for.

The Physics and Math B.A's require either the IGETC, or completion of the college of L&S requirements. The other majors you were thinking about before don't want the IGETC.

If you're sure you've narrowed it down to a math BA or physics BA from UCB, Logic doesn't fit into the IGETC requirements, so you should only take that if you have room to spare. You should also talk about enrolling for tag if UCB still does that, which they may not. I don't know.

 

[TheKracken]

Iv'e got to say that I am still undecided. I am sampling courses from every subject and seeing what I like. It will definitely be in the science/ mathematics area. For some reason I thought that this course covered a GE and I appreciate you pointing that out for me. As for the textbook, there are two different class options for me. One class the guy has written his own book and the other class requires this textbook.
https://www.amazon.com/dp/0840034172/?tag=pfamazon01-20

Now I am not sure if I will take it due to the fact it is not a GE course and will not help me...but if it would help me decide if mathematics may be up my alley then I may do so.

 

[R136a1]

Iv'e got to say that I am still undecided. I am sampling courses from every subject and seeing what I like. It will definitely be in the science/ mathematics area. For some reason I thought that this course covered a GE and I appreciate you pointing that out for me. As for the textbook, there are two different class options for me. One class the guy has written his own book and the other class requires this textbook.
https://www.amazon.com/dp/0840034172/?tag=pfamazon01-20

Now I am not sure if I will take it due to the fact it is not a GE course and will not help me...but if it would help me decide if mathematics may be up my alley then I may do so.

Ask your prof if he'll do chapters 6,7 or 8. If he does, then take the course for sure.

If he doesn't, the course might still be interesting, but maybe there are better options.

 

[TheKracken]

Could you tell me as to why those chapters are important to mathematics? Just so I can go in and talk to him about it and maybe talk to the other professor about those topics to see if he will cover those as well in his book.

 

[MathWarrior]

Definitely take that logic class; I took a very similar class. It too was a philosophy class, introduction to logic. It was one of the most useful courses I ever took; it taught you to write proofs, from a logical point of view. It is EXTREMELY useful, and I find myself using it repeatedly.

 

[R136a1]

Could you tell me as to why those chapters are important to mathematics? Just so I can go in and talk to him about it and maybe talk to the other professor about those topics to see if he will cover those as well in his book.

They are important because they constitute the basics of what is called formal logic or mathematical logic. They form the foundations of all of mathematics. It teaches you what a correct statement is, what a correct proof is. These things are of course essential in the rest of mathematics.

Obviously, you can do mathematics just fine without knowing formal logic, but I would say you're missing a whole lot of background and you're missing the big picture.

Ideally, every bit of mathematics should be brought back to predicate logic. This is of course not done in textbooks because it's very difficult to read, but you should always make sure that it can be done if you want to. This website brings all statements and proofs back to its pure form: http://us.metamath.org/

 

[Student100]

Iv'e got to say that I am still undecided. I am sampling courses from every subject and seeing what I like. It will definitely be in the science/ mathematics area. For some reason I thought that this course covered a GE and I appreciate you pointing that out for me. As for the textbook, there are two different class options for me. One class the guy has written his own book and the other class requires this textbook.
https://www.amazon.com/dp/0840034172/?tag=pfamazon01-20

Now I am not sure if I will take it due to the fact it is not a GE course and will not help me...but if it would help me decide if mathematics may be up my alley then I may do so.

Seeing as how you should plan on being in CC for two more years regardless, you should think about which major you want to do before the end summer session 2014. Some of the majors you want to do require vastly different paths to transfer.

Once you transfer to a UC system, you can't, under any circumstance that I'm aware of, change your major.

All of your paths require math through LA/DE. Most of your paths require three courses of physics, after that it branches off sharply; doing the IGETC will basically ensure you don't have time to do the biophysics prep. Without the L&S prep you can't apply for BA math/physics transfer to UCB. You should work on deciding what you want to major in sooner than later.

Logic is an interesting class like everyone is saying, it won't hurt you if you can afford the units in your timetable to transfer. I think you'll need to get your GPA higher than 3.7 to be competitive at UCB. Keep this in mind when selecting your course load.

 

[TheKracken]

I am thinking with all of those requirements for the biophysics major that I should instead either do a physics or mathematics degree. Then in graduate school if I wish to still study those topics then find a professor who does research on whatever I am interested in. Then the question is, should I do math or physics? I find mathematics much more enjoyable and find some of the topics in high level mathematics very interesting. If I do the physics or mathematics route I have enough room to add this logic course in. If I were to decide to do biophysics again then this would put me behind 3 credits. I currently have around a 3.7 in class right now and wish to actually push that higher to ensure admissions into UC Berkeley.

I appreciate everyone help. If there are any more links you all have that shows the usefulness of logic in mathematics then that would be amazing.
Thank you.

 

[TheKracken]

My professor says;

Hi Chris,

We cover truth tables and natural deduction for propositional logic, but we do not cover predicate logic. The other topics we cover include “traditional” (categorical) logic, which involves Venn diagrams for syllogisms, plus some forms of inductive argument and informal fallacies. Math majors usually do very well in logic, at least with the formal stuff.

CG

 

[R136a1]

My professor says;

Hi Chris,

We cover truth tables and natural deduction for propositional logic, but we do not cover predicate logic. The other topics we cover include “traditional” (categorical) logic, which involves Venn diagrams for syllogisms, plus some forms of inductive argument and informal fallacies. Math majors usually do very well in logic, at least with the formal stuff.

CG

Too bad they don't cover predicate logic. It seems to me that they will leave all mathy stuff out the course and that it's mostly useful for philosophers who don't need much math. I would say to take the course if you're interested. But if you want to do actual mathematics, then you should wait for another course. So don't go out of your way to take the course.

 

[MarneMath]

I don't necessary agree with R136 that the class wouldn't be helpful for a mathematician. Like I stated previously the the key part of an intro to logic course is that it teaches you to breakdown arguments into core pieces. Personally, I've always found that easy for deductive forms and harder for inductive forms. I think learning arguments and to be critical of them is a rather useful thing.

Nevertheless, if you want to see logic applied in mathematics and therefore only deductive in nature, then find a discrete math class. You'll usually cover everything you need in a book like Rosen or Epps, plus some simple proof writing.

 

[TheKracken]

Alright, I appreciate all of your help. I am still waiting on the other professor to email me back to see if she covers the better topics or not. I would probably find the course very interesting regardless, but if it will not help me directly right now and it does not cover my GE courses then I shall find some other course to take. I will have to take a discrete mathematics course during my summer or first semester of transfer to Berkeley if I decide to do mathematics anyways. My hardest problem is, when will I know if I am cut out for mathematics or would even enjoy pure math if I won't really get exposed to anything until I have already transfer d and have to stick with that major.

 

[R136a1]

Alright, I appreciate all of your help. I am still waiting on the other professor to email me back to see if she covers the better topics or not. I would probably find the course very interesting regardless, but if it will not help me directly right now and it does not cover my GE courses then I shall find some other course to take. I will have to take a discrete mathematics course during my summer or first semester of transfer to Berkeley if I decide to do mathematics anyways. My hardest problem is, when will I know if I am cut out for mathematics or would even enjoy pure math if I won't really get exposed to anything until I have already transfer d and have to stick with that major.

Generally, if you enjoy pure mathematics then you're good at it (eventually). You might not be the next Von Neumann, but that's irrelevant. Of course, if you never did anything close to pure math, then you won't know whether you're good at it. So I suggest that you spend a little of your free time working through some pure math book of your choice. I can provide good suggestions of things you can do, and I can even help you with it. If you see after a while that you enjoy the rigor and abstraction, then you're all set!

 

[MarneMath]

A good (and free!) book to help judge if you will enjoy pure mathematics is:

http://www.trillia.com/zakon1.html

Some of the topics may be hard to appreciate or swallow on your own, but if you like the general idea behind the book and solving the problems presented, you will probably enjoy the soul sucking experience of majoring in mathematics.