How do I develop a deeper understanding of physics? I'm thinking about majoring in physics, but I don't think my background is really strong at the moment. I've completed the standard first year math and physics sequence (multivariable calculus/differential equations/linear algebra and University Physics by Sears and Zemansky). I want to utilize this summer before my second year to develop a deeper and more intuitive approach to both physics and math. How do would I start this process, and what books and other resources would be useful for a self-learner?
 A: This question is a bit open-ended so I'm not sure if it's appropriate for this site, but I'll try to answer it anyway. 
What you're talking about most likely is developing so called 'maturity' in math and physics. This isn't really a well-defined concept, but most people have an intuitive sense of what it means; if you have maturity in physics this most likely means that: If you look at a physics problem, you can (usually) quickly see the best way to approach it, you know if your solution to a problem makes sense physically, you can follow proofs with relative ease and can read between the lines when looking at physical reasoning (you know what the underlying physics is when a claim is made), and you know what subtleties aren't mentioned when reading about some physics concept. 
These skills and more are what define being 'mature' in physics or math, but how do you develop them? Fortunately, this is simple. Practice, practice, practice. With more experience, and after having done more problems and learned more physics/math, all of these things come fairly naturally. So if you want to develop more physical intuition, simply spend more time on physics- doing more problems and learning more about the subject. Make your own problems, even! Question different aspects of concepts presented to you ("is this a vector or a scalar (or neither)?", "what happens to this concept in special relativity?", "is this an approximation?"). 
Resources
You're in luck. It's also helpful, in developing these skills, to read the ideas of some people who are great at physics. Four examples that you should look into:
Feynman's Lectures on Physics. These contain wonderful insights from arguably one of the best physicists of the twentieth century, and when you read them you'll definitely find new ways of looking at various aspects of physics.
Kleppner and Kolenkow- An Introduction to Mechanics. From K&K, as they're often referred to, you will first begin to really understand physics. This is a really fun book with not too many advanced concepts (you probably know all the basic physics in here already from your first year course), but what really distinguishes the book is the problems. If you can do the problems in here, you're ready for whatever physics throws at you next. They require a deep understanding of mechanics and a decent amount of ingenuity, so it's a challenge but it's also very rewarding. This is the text used in MIT's advanced first year physics course 8.012 (which used to be called "Physics for Masochists"!). This book certainly builds character, and will most likely be very helpful in developing physics intuition. 
Walter Lewin's MIT 8.01 Lectures. Lewin is a great lecturer who understands physics very well, and is very good at conveying physics clearly. You'll definitely learn from him. 
Purcell's Electricity and Magnetism. I hesitate to recommend this book because you just finished your first year... But it's amazing. It's definitely very difficult, but it is, in fact, amazing. Purcell has wonderful physical reasoning (many of his proofs of different concepts are based mostly on physical reasoning with not much fancy math). Especially interesting is his development of magnetism in this book, which is much more mature than in most standard introductory EM courses; magnetism is derived as a consequence of relativity! The problems in here are also very difficult, so it's a struggle to go through this book, but definitely a fun struggle. 
Final Remarks
If you do at least some of the things I mention above, you should be OK. The mere fact that you want to develop deeper intuition regarding physics shows that you're interested, and that's usually a good sign. Good luck, and have fun!
