Discrete Mathematics

imagine a rainbow with seven colors, you can look closely and see that the colors blend together at the boundaries and it's impossible to tell where one color begins and another ends – this is what continuous values are. Discrete mathematics is like setting down lines and saying whatever's to the left of this line is red, whatever's to the right is blue, etc.

Calculus has no overlap with discrete mathematics as calculus by its very nature – dealing with limits – is concerned with continuous variables.

You'd need to check your school's course description/syllabus to be sure, but the parts of discrete math discussed in the wiki article that would most likely be covered in a university course called "Discrete Math" include logic, set theory, combinatorics, graph theory, and discrete probability, all at a fairly introductory level (i.e. little-to-no experience with those topics will be assumed).

The only part of your experience with calculus that you'd likely draw from is the part where you watched your teacher prove things and/or read the proofs in the text; i.e. there will likely be an unstated assumption that you somewhat understand what a proof/mathematical argument looks like. It's quite common for a course in Discrete Math to serve as a kind of intro to proofs class. The topics themselves aren't particularly difficult; it's the proofs that make the class challenging.

I assume it's a discrete math for computer science, as my undergraduate cs degree had. If that is the case then you'll go through truth tables, inductive proofs, basic set stuff, basic graph theory (euler and Hamiltonian curcuits). It was a very easy class.

The Art of Problem Solving contest prep books would be complete overkill but would prepare you well for the mathematics in a CS degree.

You can use sites like MIT OCW Scholar to brush up on your calculus. Regardless of whether or not calculus is actually used in your degree, the problem solving skills one hones as you learn calculus can only be a benefit.

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If it is anything like the course at my university that CS students are required to take, it will be focused on set theory and combinatorics. No calculus needed.

I assume you speak of this class: https://www.math.vt.edu/people/mcquain/math2534.htm

So probably look over that book. Here is a list of topics covered:

1. SPEAKING MATHEMATICALLY. Variables. The Language of Sets. The Language of Relations and Functions. 2. THE LOGIC OF COMPOUND STATEMENTS. Logical Form and Logical Equivalence. Conditional Statements. Valid and Invalid Arguments. Application: Digital Logic Circuits. Application: Number Systems and Circuits for Addition. 3. THE LOGIC OF QUANTIFIED STATEMENTS. Predicates and Quantified Statements I. Predicates and Quantified Statements II. Statements with Multiple Quantifiers. Arguments with Quantified Statements. 4. ELEMENTARY NUMBER THEORY AND METHODS OF PROOF. Direct Proof and Counterexample I: Introduction. Direct Proof and Counterexample II: Rational Numbers. Direct Proof and Counterexample III: Divisibility. Direct Proof and Counterexample IV: Division into Cases and the Quotient-Remainder Theorem. Direct Proof and Counterexample V: Floor and Ceiling. Indirect Argument: Contradiction and Contraposition. Indirect Argument: Two Classical Theorems. Application: Algorithms. 5. SEQUENCES, MATHEMATICAL INDUCTION, AND RECURSION. Sequences. Mathematical Induction I. Mathematical Induction II. Strong Mathematical Induction and the Well-Ordering Principle. Application: Correctness of Algorithms. Defining Sequences Recursively. Solving Recurrence Relations by Iteration. Second-Order Linear Homogeneous Recurrence Relations with Constant Coefficients. General Recursive Definitions and Structural Induction. 6. SET THEORY. Set Theory: Definitions and the Element Method of Proof. Set Identities. Disproofs and Algebraic Proofs. Boolean Algebras, Russell's Paradox, and the Halting Problem. 7. PROPERTIES OF FUNCTIONS. Functions Defined on General Sets. One-to-one, Onto, Inverse Functions. Composition of Functions. Cardinality, Sizes of Infinity, and Applications to Computability. 8. PROPERTIES OF RELATIONS. Relations on Sets (add material about relational databases). Reflexivity, Symmetry, and Transitivity. Equivalence Relations. Modular Arithmetic with Applications to Cryptography. Partial Order Relations. 9. COUNTING. Counting and Probability. The Multiplication Rule. Counting Elements of Disjoint Sets: The Addition Rule. The Pigeonhole Principle. Counting Subsets of a Set: Combinations. r-Combinations with Repetition Allowed. Pascal's Formula and the Binomial Theorem. Probability Axioms and Expected Value. Conditional Probability, Bayes' Formula, and Independent Events. 10. GRAPHS AND TREES. Graphs: An Introduction. Trails, Paths, and Circuits. Matrix Representations of Graphs. Isomorphisms of Graphs. Trees: Examples and Basic Properties. Rooted Trees. Spanning Trees and a Shortest Path Algorithm. 11. ANALYZING ALGORITHM EFFICIENCY. Real-Valued Functions of a Real Variable and -Notations. Application: Efficiency of Algorithms I.?-, and ?Their Graphs. O-, Exponential and Logarithmic Functions: Graphs and Orders. Application: Efficiency of Algorithms II. 12. REGULAR EXPRESSIONS AND FINITE STATE AUTOMATA. Formal Languages and Regular Expressions. Finite-State Automata. Simplifying Finite-State Automata.