- #1
rxh140630
- 60
- 11
How is one suppose to study advanced subjects when often textbooks that cover advanced subjects don't even have answers to the exercises?
Once you progress to material that is at your limit of understanding it's very difficult with no support other than the textbooks and internet resources.rxh140630 said:How is one suppose to study advanced subjects when often textbooks that cover advanced subjects don't even have answers to the exercises?
Vanadium 50 said:Usually it's the reverse - it takes longer to develop an understanding (if it happens at all) with self-study.
PeroK said:Once you progress to material that is at your limit of understanding it's very difficult with no support other than the textbooks and internet resources.
It's tough, I know.
I cannot agree more.Stephen Tashi said:I think a big reason for slowness is that a person who self-studies can become a prisoner of his personal concept of what understanding is. For example, a self-studier may wish to have an intuitive understanding or, more rarely, a completely rigorous understanding. In a course, material is explained by giving some mode understanding and that is usually sufficient to deal with the course. Students adapt their personal tastes about understanding to include methods they see other people using. They must broaden their concept of what understanding is.
By contrast a person studying alone may want to have everything explained in a certain way - for example, in a geometric or visual way. If he tries to read a textbook where the mode of explanation is different - for example, one that emphasizes symbolic manipulations - then he doesn't have the benefit of a teacher and classmates to show him the variety of ways in which things can be understood.
How advanced? If you are talking about general undergraduate subjects, I am a big fan of Schaum's Outlines. They always have a lot of worked examples and exercises.rxh140630 said:How is one suppose to study advanced subjects when often textbooks that cover advanced subjects don't even have answers to the exercises?
symbolipoint said:rxh140630,
Can you be specific about what topic subject, and what textbook? The responses you receive might be more clear.
Leo Liu said:I cannot agree more.
I didn't understand probability while taking a stat class in high school because the concepts seem quite counter-intuitive. I got 60ish on my first test and 70ish on my second test. I was worried about my grade so I asked a friend who did fairly well in my class to help me with it. He showed me his understanding of probability, and afterwards I got a low 90 on my midterm without spending too much time on the exam preparation.
As you can see, a helpful peer can even save one's grade.
FactChecker said:How advanced? If you are talking about general undergraduate subjects, I am a big fan of Schaum's Outlines. They always have a lot of worked examples and exercises.
I think that you should look at the Schaum's Outline series. I used them to drill for the Ph.D. candidate acceptance tests. That being said, I just used the problems for drills, not the text for understanding, which I already had.rxh140630 said:Graduate level math/physics.
Can you explain what you meant by this?rxh140630 said:not meaning to apply that there isn't a correlation between the grade that you receive and understanding though.
rxh140630 said:How is one suppose to study advanced subjects when often textbooks that cover advanced subjects don't even have answers to the exercises?
vanhees71 said:Well, without "teacher solution books" the teachers are even more lost than the students. I had a high school teacher who claimed we had wrong answers in a test, but there were several of us having the same answer, which would be quite improbable if the answer were really wrong. Arguing with the teacher we calculated everything in great detail on the black board. After that she admitted that it sounds right, but she cannot tell with certainty. She had another answer to the question in her teacher's solution book! It ended up with asking another teacher at our school about his opinion, and it turned out we were right. So whenever you write a textbook at least provide correct answers to the teachers, because otherwise many may be lost!
Infrared said:@Math_QED I actually want to give the teacher some credit. When confronted with an issue she didn't understand, she admitted to the students that she wasn't sure, sought clarification from someone who knew, and then communicated her finding to her students. This seems to be exactly the right course of action (as opposed to pretending to know that she's right, etc.).
vanhees71 said:but there were several of us having the same answer, which would be quite improbable if the answer were really wrong.
Infrared said:She apparently thought that she understood the problem, and then realized she was mistaken. I'd forgive this as human error. I've had several professors assign problems with errors, and I certainly don't judge their teaching ability (or mathematical understanding) on it.
Math_QED said:I'm speaking high school here.
She was a night mare. She couldn't even demonstrate the solution of a linear system of equations with 2 variables...Math_QED said:Sounds like a really bad high school teacher.
jtbell said:In the US, how many high-school physics teachers actually have a bachelor's degree in physics?
This advice is almost the same as what I was going to give. I was going to say to go to a local college's math tutor department, while it is not busy, and ask if someone will check your work. In my experience, they just assume that I go to the school. Once you know what the right solution is, whether you figured it out, or received it from the tutor, or received it from here, put it in a notebook Then refer to it when you practice to use as a reinforcement to your response for the excercise.gleem said:You could work out the problems and submit them for review at PF. Show your work and approach to get feedback.
Studying advanced subjects without answers refers to the process of learning and exploring complex ideas and concepts that do not have a definitive solution or answer. It involves critical thinking, analysis, and interpretation of information.
Studying advanced subjects without answers helps to develop critical thinking skills, encourages creativity and innovation, and promotes a deeper understanding of complex topics. It also prepares individuals to tackle real-world problems that do not have a clear solution.
Examples of advanced subjects without answers include philosophy, theoretical physics, sociology, and psychology. These fields deal with complex and abstract concepts that do not have a definitive answer.
One can approach studying advanced subjects without answers by being open-minded, asking questions, and critically analyzing information. It is also essential to engage in discussions and debates with others to gain different perspectives and deepen understanding.
Studying advanced subjects without answers can improve problem-solving skills, enhance creativity, and foster a deeper understanding of complex topics. It also prepares individuals for a rapidly changing and evolving world where there may not always be a clear answer or solution.