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21-127 Concepts of Mathematics Fall or Spring: 9 units By the end of this course the student should be able to - Construct logically correct proofs using basic proof techniques such as proof by contradiction.
- Deploy basic problem solving strategies.
ax + by =c. Congruences,
modular arithmetic. Recursion. Linear recurrences. Functions and inverses.
Permutations. Binomial coefficients, Catalan number. Inclusion-exclusion. Infinite
cardinalities. Binary operations. Groups. Binary relations, equivalence relations.
Graphs. Euler characteristic, planar graphs, five color theorem, rationals, reals,
polynomials, complex numbers.
3 hours lecture, 2 hours recitation. No prerequisites. A prerequisite for 15-211, 21-341, 21-228, 21-355 and other mathematics courses requiring the construction of proofs. A co-requisite for 18-240. Recommended as a prerequisite for 21-241. |