Rudin's "Principals of Mathematical Analysis" is an excellent intro to real analysis for self-study. Axler's "Linear Algebra Done Right" is good for linear alg

Rudin's "Principals of Mathematical Analysis" is an excellent intro to real analysis for self-study. Axler's "Linear Algebra Done Right" is good for linear algebra. Neither makes any effort to bridge the gap between theory and application, so if that is a difficulty, you might need other texts as well.