Hello! I have occasionally lurked this forum and have found some really interesting discussions. I finally decided to join the forum and also wanted to start off with a question. I have a bachelors degree in mechanical engineering so I have the mathematics and physics foundation typically achieved with that degree. I have also worked in a variety of industries for about 15 years, and have continued to apply statics and fluid mechanics in a variety of design and analysis projects. Unfortunately, this leads me to being quite rusty in electromagnetism and optics, as well as having had very little reinforcement of math skills beyond some basic calculus over the past decade. Also, when I was in undergraduate, we spent very little time with modern physics areas. I am in the situation now where I have some time that I want to dedicate to catching up with all the physics that I forgot, as well as start tackling modern physics areas that I have always found extremely fascinating but never had a chance to study in depth. At the moment, I am just going through the Young and Freedman University Physics book, one chapter at a time and doing problems. But I was wondering if any of you recommend that I also review calculus, differential equations, and linear algebra and other areas of math? Or should I just study physics and refer to math books only if and when I get stuck? My hope is that once I get through the textbook, I can explore other areas like condensed matter, quantum mechanics, particle physics, etc. The main reason I want to study all of this is because as much as I have enjoyed the projects I have worked on, there are a lot of areas of physics I absolutely loved in college and I want to have a chance to explore some other areas. Also, my career has been pretty good to me over the years and I am in a situation where I want to pursue new things and less concerned about salary. So my goal is that my self-study can inspire me to get into an area of physics that I might want to research and maybe lead me to grad school opportunities. Any recommendations on areas of mathematics to consider, and/or math or physics textbooks would be appreciated! Thank you!