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I am a sophomore with double majors in microbiology and mathematics (just declared on last week) doing research on the computational/quantitative biology research in the field of virology. In future, I want to go to a graduate school in either virology or computational biology that focus on both numerical approach and "wet experimental" approach to science. I just declared my second major in mathematics on last week since I thought that having a quantiative/analytic background like mathematics would be very helpful than chemistry or physics (which I was planning to major until my decision for mathematics). I have been planning to do a self-study on the mathematics, particularly the calculus, which I want to start as soon as this semester ends. I know a lot of working.computational knowledge in the vector calculus, linear algebra, differential equations, and discrete mathematics, but my mathematical knowledge is sporadic and non-systematic. My mathematics adviser also recommended me to do some self-study so I can effectively prepare for my multi-variable calculus and linear algebra courses on next semester. Unfortunately, my only mathematics course is a first semester of typical single-variable calculus course which I took on last year's Fall; I was not able to proceed to the second semester after that since I took many chemistry courses to satisfy my chemistry major (which I am not pursuing now). My math adviser told me I can proceed to multi-variable calculus & linear algebra on next semester if I am comfortable, and I agreed to do an extensive self-study on the necessary materials. I have a following studying plan I will start as soon as early December, which I would like to have your input for self-studying:

"A First Course in Calculus" (Serge Lang) + "How to Prove It" (Velleman) + "Basic Mathematics" (Serge Lang) -----> Apostol Vol.1 vs. Spivak. vs Courant. Do I need to read the "easier" single-variable calculus textbook like A First Course in Calculus by Serge Lang along with the How to Prove It by Velleman and Basic Mathematics by Lang before proceeding to Apostol/Spivak/Courant? I would like to start with those rigorous books but I heard that it is quite difficult to do so. I do have a working knowlegde in mathematics as I stated on the first paragraph, which I grasped through the book called "Mathematical Methods for Physical Science" by Mary L. Boas. In this case, should I still read those three preparatory books before Apostol,Spivak, and Courant? Between Apostol/Spivak/Courant, which textbook has a most detailed contents in calculus along with some applications? I heard that all three books lack in applications but I can supplement them with the problems book like Schaum or normal calculus textbooks like Stewart.

My multi-variable calculus course uses the eTextbook (made from the Department of Mathematics) and linear algebra uses a book called "Linear Algebra" by Friedberg. Is it okay to supplement the multi-variable calculus course with the "Calculus of Several Variables" by Serge Lang + Calculus Vol.II by Apostol? What about my linear algebra textbook? Can I supplemtn Friedberg with Apostol too?

I apologize for this long post and any grammatical errors. I look forward to your advice!

Sincerely,