College Guidance: Struggling with Math & Physics in College

[dogtail]

I just need some direction. I just can't seem to solve anything in math or physics right now. I want to become good at both but I just am struggling mightily. First year in college in mechanics and calculus. Every one says to just work harder. This is very frustrating because I put in over 10 hours a day on pure studying, outside of the lectures. All this work and I still can't get it. I am starting to feel that I'm just not good enough. Does anybody here have some words of wisdom that can help me out.

 

[symbolipoint]

I just need some direction. I just can't seem to solve anything in math or physics right now. I want to become good at both but I just am struggling mightily. First year in college in mechanics and calculus. Every one says to just work harder. This is very frustrating because I put in over 10 hours a day on pure studying, outside of the lectures. All this work and I still can't get it. I am starting to feel that I'm just not good enough. Does anybody here have some words of wisdom that can help me out.

Your preparation is not good enough, most likely. You said nothing about your high school courses nor any preparation while in college. Calculus can be difficult. Physics 1 (Mechanics, beginning, calculus-based) can be difficult. Anywhere along the sequence of the prerequisite mathematics courses could be a tough transitional course. Physics 1, itself is also a tough transitional course in that you must become a detailed, analytical thinker, very confident in your use of applying the intermediate level of Algebra.

You may need to repeat some prerequisite courses if you really want a mathematical or physics-related university degree. Merely having credit in them means nothing or very little. What is important is your current competence in them.

 

[KiggenPig]

It's normal to hit rough patches - don't let it discourage you. Remember persistence pays off.
But I must echo what symbolipoint pointed out, as there is likely an issue with the fundamentals somewhere down the line.
Perhaps if you could expand a little - let us know if you struggle with the mathematics or what?

 

[dogtail]

Yes I did take calculus in high school and our finals were the same final as a local college. Both semesters I got 100%. I took AP chem and got a 5. I took physics but my school didn't have AP and the class was a complete joke. I got a 105% in it and never even felt like I had a firm understanding of it so obviously we weren't pushed very much. I've always just naturally been intrigued by the way things work and I've always wanted to be a physicist. It is the only thing that holds any importance for me. Due to success in high school calc I felt I had a good platform to build on but now at university it is much harder and the problems are much more complex. I am having trouble visualizing what the problem means or the direction I should go to solve the problem. I am very discouraged but I think that if I can get it to click that I can do great just because I am so passionate about it. This passion has also led to some hard times because I have gotten really down on myself scared that I will never get to live my life understanding physics on a deep level. Learning and understanding these things is the only thing that makes me happy. In high school our chem teacher gave us an equation that this college professor would give his chem students an hour to balance and if they did he would give them an A. I didn't finish it in an hour haha but I took it home and after 5 hours I got it and it was the happiest I have ever been. This is why I am scared I will end up failing and live my life miserably because nothing else can give me satisfaction really.

 

[dogtail]

Once I know the route to take my algebra is very good I believe. I just lack creativity sometimes or the natural solving ability. If I can see or realize how something works I can usually solve it from there. This has helped me solve some challenge problems in high school that no one but me could get. It's not that I was smarter but I was relentless and wouldn't stop until I had solved the problem. I hate memorizing how to solve 100 different types of problems. I want to be able to grasp these topics on a deeper conceptual level so that I can then apply my knowledge to any problem. Not just ones that are similar or the same to ones I've seen before. In high school I did this but the ideas were less abstract/complex and the pace wasn't as heavy so now I am having difficulties.

 

[Student100]

What exactly are you struggling at? How are other students performing?

Post an example problem.

 

[dogtail]

Other students find the calculus difficult but that doesn't really matter for me. I don't want to find ease in other students problems.

But most problems for me are doing problems where you really have to deeply understand the mathematical principles. I can take derivatives and integrals and all that but one problem for example right now,

An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t). Assume 0<t<pi/4. At a given time t the tangent line to the unit circle at the position p(t) will determine a right triangle in the first quadrant. Connect the y and x intercepts of the tangent line.

The area of the right triangle is a(t)=?
The derivative a'(t)=?
At what time is the rate of change of the area of the triangle zero?
At what time is the area of the triangle 4?

Or another one:
An object is moving back and forth on the x-axis according to the equation x(t)=3sin(20pi t), t>0, where x(t) is measured in cm and t in seconds.
How many complete back and forth motions does the object take in 1 second?
What is the time the object is at the furthest right?

These are examples of what I'm struggling with. Taking situations and being able to apply the calculus to them. I know the calculus because of high school. I just can't apply it very well.

 

[symbolipoint]

Read your posts, #4, #5, #7.
You analyzed your trouble and have figured what to do, maybe.
Creativity is less important (NOT unimportant) than critical thinking, attention to detail, effectiveness in analyzing, and fitting the mathematical properties or formulas needed for a situation.

Jumping from high school straight into college level mathematics at Calculus 1 could be a problem. Preliminary placement testing should have been done to check if this could be a troublesome problem to expect. Mathematics is extensively mingled into Physics at a very high extent. YOU must be skillful with intermediate algebra, most of trigonometry, simple basic linear algebra, and obviously some of first-year college Calculus. I made earlier mention of course repetition. This might be a possible fix for you, but really, you could restudy some courses on your own if below the mid-year Calculus level.

See officials in your Math or Physics department for counseling. Some of them can get better access to you and your work and records.

 

[Student100]

Other students find the calculus difficult but that doesn't really matter for me. I don't want to find ease in other students problems.

But most problems for me are doing problems where you really have to deeply understand the mathematical principles. I can take derivatives and integrals and all that but one problem for example right now,

An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t). Assume 0<t<pi/4. At a given time t the tangent line to the unit circle at the position p(t) will determine a right triangle in the first quadrant. Connect the y and x intercepts of the tangent line.

The area of the right triangle is a(t)=?
The derivative a'(t)=?
At what time is the rate of change of the area of the triangle zero?
At what time is the area of the triangle 4?

Or another one:
An object is moving back and forth on the x-axis according to the equation x(t)=3sin(20pi t), t>0, where x(t) is measured in cm and t in seconds.
How many complete back and forth motions does the object take in 1 second?
What is the time the object is at the furthest right?

These are examples of what I'm struggling with. Taking situations and being able to apply the calculus to them. I know the calculus because of high school. I just can't apply it very well.

It's not about finding solace in other students, it's about gauging the class. If you believe you can earn an A on every exam through your undergrad you're sorely mistaken. I've earned low F's (40's) on exams which were really in the top 5% of the class. I didn't worry that I wasn't getting the other 60 some odd percent of the test correct right away. Some professors do this in university, so I always found it a good idea to see where you rank in comparison to your peers.

Neither of the problems require "deep understanding on mathematical principles", they only require experience solving problems. For the first problem you just need to draw the picture. The second problem just requires you understand that it's oscillating, again draw a picture.

You're over thinking all this, and you have to identify that your problem is a lack of experience, not something fundamental with yourself. My advice is to make sure that those ten hours you're studying are used mostly solving problem sets.

 

[dogtail]

I did take a math placement test and did very well. I make very few mathematical mistakes when just doing straightforward problems but it is the critical thinking, effectiveness in analyzing, and fitting principles together that I with. I know all the principles up to the math I am now in. I just can't seem to solve the type of problem like the ones i posted. How would you approach these? i just can't figure it out.

 

[symbolipoint]

I did take a math placement test and did very well. I make very few mathematical mistakes when just doing straightforward problems but it is the critical thinking, effectiveness in analyzing, and fitting principles together that I with. I know all the principles up to the math I am now in. I just can't seem to solve the type of problem like the ones i posted. How would you approach these? i just can't figure it out.

You may be making the adaptation now, in your current course. Either you will gain some success or you will not. None of us know. You need to do as well as you can to make your way through the course. After that, either (1) repeat the whole course on your own (but no laboratory) if you pass, or (2) repeat the course officially if you do not pass. A student does better in a course when he enrolls in it one more time.

 

[symbolipoint]

I did take a math placement test and did very well. I make very few mathematical mistakes when just doing straightforward problems but it is the critical thinking, effectiveness in analyzing, and fitting principles together that I with. I know all the principles up to the math I am now in. I just can't seem to solve the type of problem like the ones i posted. How would you approach these? i just can't figure it out.

This means you have the necessary academic qualifying credit but you do not have the right amount of or the right kind of mathematical conditioning. One thing about studying Physics 1 - fundamental mechanics, is that this makes Mathematics more REAL for you.

 

[dogtail]

It's not about finding solace in other students, it's about gauging the class. If you believe you can earn an A on every exam through your undergrad you're sorely mistaken. I've earned low F's (40's) on exams which were really in the top 5% of the class. I didn't worry that I wasn't getting the other 60 some odd percent of the test correct right away. Some professors do this in university, so I always found it a good idea to see where you rank in comparison to your peers.

Neither of the problems require "deep understanding on mathematical principles", they only require experience solving problems. For the first problem you just need to draw the picture. The second problem just requires you understand that it's oscillating, again draw a picture.

You're over thinking all this, and you have to identify that your problem is a lack of experience, not something fundamental with yourself. My advice is to make sure that those ten hours you're studying are used mostly solving problem sets.

That's what is frustrating though- I do spend all my time trying to solve problems and I encounter two types of problems, problems like take the derivative of find the integral, or balance this equation, and usually on these I can solve these even if they are considered hard. But then the other problems, word problems like the ones I posted, I have no idea where to start. Its like I can do the "math" part of it but I can't do problems when its not a specific task like take the derivative. I don't know why it is, if I did I wouldn't be posting on here.

 

[dogtail]

This means you have the necessary academic qualifying credit but you do not have the right amount of or the right kind of mathematical conditioning. One thing about studying Physics 1 - fundamental mechanics, is that this makes Mathematics more REAL for you.

I feel like that is what I'm struggling with. Going from straightforward high school problems to more real life stuff. I want to condition myself to do these problems I just don't know how. It seems like my efforts are getting me no where.

 

[Student100]

That's what is frustrating though- I do spend all my time trying to solve problems and I encounter two types of problems, problems like take the derivative of find the integral, or balance this equation, and usually on these I can solve these even if they are considered hard. But then the other problems, word problems like the ones I posted, I have no idea where to start. Its like I can do the "math" part of it but I can't do problems when its not a specific task like take the derivative. I don't know why it is, if I did I wouldn't be posting on here.

I told you what it is, it's experience and heuristics. I was the same way when I first started, a very good calculator but I couldn't set up wordy problems. The only way to get better is to keep trying at those problems.

Draw pictures and diagrams, think about the nature of what the problem is trying to tell you. For the first example you gave, you'd draw a unit circle in the typical Cartesian coordinate system. A line that's tangent to a location on the circle can be drawn in which the line intersects both the x and y-axis in the first quadrant forming a right triangle. The picture basically sets up the entire problem for you.

Then you can write out what you need to know and what you know, etc. There is usually a whole spiel dedicated to these heuristic techniques at some point during your mechanics class. Once you gain more experience with these problems you don't necessarily have to follow them as they generally aren't the most optimal way to find the solution, but can be helpful when you have no idea how to start.

 

[dogtail]

I told you what it is, it's experience and heuristics. I was the same way when I first started, a very good calculator but I couldn't set up wordy problems. The only way to get better is to keep trying at those problems.

Draw pictures and diagrams, think about the nature of what the problem is trying to tell you. For the first example you gave, you'd draw a unit circle in the typical Cartesian coordinate system. A line that's tangent to a location on the circle can be drawn in which the line intersects both the x and y-axis in the first quadrant forming a right triangle. The picture basically sets up the entire problem for you.

Then you can write out what you need to know and what you know, etc. There is usually a whole spiel dedicated to these heuristic techniques at some point during your mechanics class. Once you gain more experience with these problems you don't necessarily have to follow them as they generally aren't the most optimal way to find the solution, but can be helpful when you have no idea how to start.

Ok thank you for the advice. I actually am not really having any huge problems in physics just because the word problems with like forces or projectile motion or kinematics i can visualize and then use the equations and manipulate variables. Although our first midterm was tough because it was like 20 questions in only 1 hr and i didn't really have time to think or reason things out. But Its really the pure math word problems that trip me up.

 

[symbolipoint]

Ok thank you for the advice. I actually am not really having any huge problems in physics just because the word problems with like forces or projectile motion or kinematics i can visualize and then use the equations and manipulate variables. Although our first midterm was tough because it was like 20 questions in only 1 hr and i didn't really have time to think or reason things out. But Its really the pure math word problems that trip me up.

?
?
Learn to draw pictures, diagrams, and figures. A visualization will not always come to you immediately upon a first-reading of a word-described problem. You may need to read and reread it before you understand it well enough to develop a picture with parts to label.

We are animals. A discussion in another thread or topic has pointed to this. We are animals, and we still do think in pictures. We as scientists think in both pictures and in symbols. You can check this forum thread: https://www.physicsforums.com/threads/animal-communication.837750/

 

[dogtail]

?
?
Learn to draw pictures, diagrams, and figures. A visualization will not always come to you immediately upon a first-reading of a word-described problem. You may need to read and reread it before you understand it well enough to develop a picture with parts to label.

We are animals. A discussion in another thread or topic has pointed to this. We are animals, and we still do think in pictures. We as scientists think in both pictures and in symbols. You can check this forum thread: https://www.physicsforums.com/threads/animal-communication.837750/

ok thanks. May I ask what the question marks are for?

 

[symbolipoint]

ok thanks. May I ask what the question marks are for?

Trying to understand the second sentence in what I quoted, and not really knowing how visualizing and drawing pictures are different for you. "I actually am not really having any huge problems in physics just because the word problems with like forces or projectile motion or kinematics i can visualize and then use the equations and manipulate variables." You must not expect to be able to hold all visualizations in your head. You may often need to understand what you read and form into a picture and label the parts. A second question mark is about wondering if you "had not enough time to think or reason things out" is a guess that you did not practice enough or do enough exercises. I really not yet have enough detailed knowledge of how you work, study, practice, or how or why making drawings or diagrams is making the work more difficult for you, - or IF it is making anything difficult for you. Not enough time to think through the exam questions can be either that the exam was too long or that you have some trouble analyzing and drawing pictures for what you read, and again, I do not know why this is for YOU.
AFTER the question marks, I tried to tell you what makes the best sense.

Physics 1, as I said already, is a transformative course which should turn you into a more analytical thinker and better problem-solver.

 

[dogtail]

Trying to understand the second sentence in what I quoted, and not really knowing how visualizing and drawing pictures are different for you. "I actually am not really having any huge problems in physics just because the word problems with like forces or projectile motion or kinematics i can visualize and then use the equations and manipulate variables." You must not expect to be able to hold all visualizations in your head. You may often need to understand what you read and form into a picture and label the parts. A second question mark is about wondering if you "had not enough time to think or reason things out" is a guess that you did not practice enough or do enough exercises. I really not yet have enough detailed knowledge of how you work, study, practice, or how or why making drawings or diagrams is making the work more difficult for you, - or IF it is making anything difficult for you. Not enough time to think through the exam questions can be either that the exam was too long or that you have some trouble analyzing and drawing pictures for what you read, and again, I do not know why this is for YOU.
AFTER the question marks, I tried to tell you what makes the best sense.

Physics 1, as I said already, is a transformative course which should turn you into a more analytical thinker and better problem-solver.

Ok, sorry I was too vague. I do draw pictures and diagrams but I didn't really explain myself too well. I meant to say that real life things like motion, or forces I can wrap my head around and then model the situation, with a free body diagram or a small picture and label all the forces, the initial heights, the maximum heights to an approximation, etc. But the problems that are purely mathematical found in calculus and deal with nothing other than equations, i can not draw out or picture as well. Like i said I'm not doing terrible in physics. I wouldn't say I'm doing terrible in math either, I just want to become better at both of them. When i posted this earlier it may have sounded like I was doing terrible. this is because i had just come off trying 3 or 4 problems that i couldn't do and i started to panic with all the tests we are having right now. I can get down on myself pretty easily and haven't really been able to satisfy myself, even when I am succeeding because I know in reality I am not doing anything special at all. Anyways, the test itself wasnt terribly hard in hindsight but during it, due to the abnormal length, made it very stressful. I felt that i was very prepared. I had taken the MIT and Amherst mid term exams as a way to test myself and i got above 95% on both of them but the tests were only 5 questions each (with an a,b,and c to them). Our test was like 20 problems and a few of the people i talked to didnt even finish it. On the problems i didnt understand right away I sort of rushed into working them out due to time constraints. Because of the curve I believe I will at least get a C worst case scenario but I think i will do better than that but who knows maybe i did worse i don't want to get my hopes up. Anyway, time constraints have always been a big issue of mine. In AP chem on our first test we only had an hour and i got like a 75% which i wasnt too happy about. The rest of the year the teacher gave us an hour and a half (first period, came in early) and I set the record for the most aced tests in a row. I am not trying to brag or anything, I know its just general chemistry but the time constraint really stressed me out