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MTH 223: Calculus and Analytical Geometry III
3.00 Credits
Providence College
1 semester, 3 credits ( Mathematics Core) This course is required for all mathematics, EPS, and chemistry majors, and is recommended for biochemistry majors. A continuation of MTH 132.The main topic is multivariable calculus. Prerequisite: MTH 132.
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MTH 223 - Calculus and Analytical Geometry III
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MTH 301: Foundations of Mathematics
3.00 Credits
Providence College
1 semester, 3 credits This course is designed to aid the student in the transition from calculus to the study of advanced courses in mathematics.Topics in logic, set theory, relations, functions, cardinality, and algebra will be discussed. Emphasis will be placed on the rigorous deductive process pervasive in the study of mathematics. Prerequisite: Calculus or permission of instructor.
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MTH 301 - Foundations of Mathematics
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MTH 302: Topics in Mathematical Logic
3.00 Credits
Providence College
1 semester, 3 credits An introduction to aspects of logic appropriate to both the mathematics and computer science student.Topics in propositional and predicate logic, formal theories, computability, and metamathematics will be discussed. Prerequisite: Calculus or permission of instructor.
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MTH 302 - Topics in Mathematical Logic
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MTH 304: Differential Equations
3.00 Credits
Providence College
1 semester, 3 credits Theory of linear differential equations and methods of solution, including series and transforms. Prerequisite: MTH 223.
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MTH 304 - Differential Equations
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MTH 307: Combinatorial Theory
3.00 Credits
Providence College
1 semester, 3 credits An introduction into the basic techniques of combinatorial mathematics including fundamental enumeration principles and algebraic counting techniques.
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MTH 307 - Combinatorial Theory
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MTH 309: Geometry
3.00 Credits
Providence College
1 semester, 3 credits This course aims to familiarize the student with the principles of deductive reasoning through geometry.Topics include a review of the basic concepts encountered in Euclidean geometry and an historical development of non-Euclidean geometry.
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MTH 309 - Geometry
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MTH 315: Abstract Algebra I
3.00 Credits
Providence College
1 semester, 3 credits Topics include: basic properties of groups, Cayley tables, finite and infinite groups, abelian and non-abelian groups, subgroups, cyclic groups, symmetric and dihedral groups, matrix groups, group isomorphisms, group homomorphisms, Lagrange's theorem, normal subgroups and factor groups, the First IsomorphismTheorem, direct products. Prerequisites: MTH 215 and 301.
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MTH 315 - Abstract Algebra I
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MTH 316: Abstract Algebra II
3.00 Credits
Providence College
1 semester, 3 credits Topics include: properties of rings, integral domains, rings with non-zero characteristic, ring homeomorphisms, polynomial rings, ideals, principal ideal domains, prime and maximal ideals, factor rings, factoring polynomials, unique factorization domains, Euclidean domains, introduction to field extensions and finite fields. Prerequisite: MTH 315.
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MTH 316 - Abstract Algebra II
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MTH 317: Number Theory
3.00 Credits
Providence College
1 semester, 3 credits An investigation into the basic properties of the integers. Topics include sums of squares, divisibility, the Chinese remainder theorem, and quadratic reciprocity law.
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MTH 317 - Number Theory
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MTH 323: Real Analysis I
3.00 Credits
Providence College
1 semester, 3 credits Axioms for the real numbers, topology of the real numbers, Heine-Borel theorem, Bolzano-Weierstrass theorem, continuous and uniformly continuous functions, extreme and intermediate value theorems, differentiable functions, mean value theorem,Taylor's theorem. Prerequisite: MTH 110, MTH 132, or MTH 223 and MTH 301.
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MTH 323 - Real Analysis I
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