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Math

Math

First Year

Finished!

First semester

  • Dicrete Maths
    • Discrete Mathematics with Applications, 2nd edition by Susanna S. Epp
    • Discrete Mathematics Structures, 4th edition by Kolman, Busby and Ross
  • Proof writing (very advanced, do not expect to master anything in these books)
    • Mathematical Proofs: A transition to advanced mathematics by Gary Chartrand et. al (This one is better than the next one)
    • An introduction to Abstract Mathematics by Robert J. Bond and Wiliam J. Keane

Second semester

  • Pre-algebra (refresh really basic math)
    • AGS Pre-Algebra (has solutions)
    • Fearon’s Pre-Algebra (this one is better)
  • College Algebra (after the pre-algebra one, if the pre-algebra books are too easy skip onto these ones)
    • College Algebra by Kaufmann (more begginer friendly)
    • College Algebra by Blitzer
Second Year

WIP

First semester

  • Pre-calculus (once you are done with college algebra. If you know some basic algebra you can skip the college algebra and start in this section)
    • A Graphical Approach to Algebra and Trigonometry by Hornsby, Lial, and Rockswold. 6th edition (Get the instructor’s edition)

Second semester

  • Calculus
    • [O] Calculus by James Stewart, 5th edition (Very famous book, to learn basic calculus. It has a lot of problems. Used to teach calculus I, II and III)
    • Calculus by Michael Spivak, 3rd edition (It has less material but it is more advanced)
Third Year

First semester

  • Differential equations
    • [O] A First Course in Differential Equations by Zill
    • Ordinary Differential Equations with Applications by Andrews (It is easier, good for beginners)
  • Linear Algebra (try to learn as much as possible)
    • [O] Elementary Linear Algebra by Howard Anton (Beginner friendly, with exercises)
    • [O] Linear Algebra by Friedgber, Insel, and Spence (It is harder and more difficult to read. It is proof based)

Second semester

  • Statistics
    • [O] Mathematical Statistics by Wackerly, Mendenhall, and Scheaffer
    • [O] A First Course in Probability by Ross
  • Complex analysis (Calculus with complex numbers. Both are pretty much the same, very good beginner books)
    • Fundamentals of Complex Analysis by Saff and Snider, 3rd edition
    • [O] Complex Variables and Applications by Brown and Churchill, 7th edition
Fourth Year

First semester

  • Real analysis (one of the hardest subjects)
    • Analysis 1 and Analysis 2 by Terrance Tao (Easier to read, but the other two are standard)
    • Advanced Calculus by Fitzpatrick
    • Principles of Mathematical Analysis by Rudin
    • Elements ofAnalysis by Ross (Expends a lot of time for proofs)
  • Abstract algebra (study of groups, rings and fields. Very proof based)
    • Abstract Algebra by Saracino (Very good for beginners)
    • Contemporary Abstract Algebra by Gallian (Also good for beginners)

Second semester

  • Topology (optional)
    • Introduction to Topology by Gamelin and Greene (It has full solutions for all of the problems)
  • Combinatorics (optional)
    • Applied Combinatorics by Tucker
  • Naive set theory (optional)
    • Naive Set Theory by Halmos
  • Functional analysis (optional)
    • Functional Analysis by Kreyszig
  • Graph Theory (optional)
    • Graph Theory by Gould
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