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MT 317: Mathematical Models in Physical Science
3.00 Credits
Alverno College
Prereq. SC 117 or SC 119 - This integrated mathematics and physical science course for elementary education majors with a support in mathematics or science assists the student in reaching two objectives: a strengthened understanding of mathematics and physical science, and experience in developing teaching strategies that use the integrated approach she is experiencing. A variety of physical experiments teach about linear, quadratic, exponential, and trigonometric relationships in a practical, hands-on way.
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MT 317 - Mathematical Models in Physical Science
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MT 340: History of Mathematics
2.00 Credits
Alverno College
Prereq. For MT majors, MT 253; for ELM/mtm and ELC/mte majors, MT 221 or MT 243 or MT 244 - The student studies the history of mathematics as it is embedded in the development of world cultures. Contemporary mathematical events and trends are placed in historical context. The student spends significant time analyzing problem-solving methods and using them to solve problems from given times and cultures.
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MT 340 - History of Mathematics
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MT 345: College Geometry
3.00 Credits
Alverno College
Prereq. For ELC and ELM majors: MT 244; for MT/sed majors: MT 253 - In this course, the student works with Euclidean geometry in two dimensions. She uses visualization, spatial reasoning, and geometric modeling to solve problems. Technology tools are employed to explore ideas and generate conjectures, leading to mathematical proofs.
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MT 345 - College Geometry
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MT 347: Modern Algebra
4.00 Credits
Alverno College
Prereq. MT 253 - The student learns to identify abstract algebraic structures such as groups, rings, and fields and to use their defining axioms. She explores the properties of these systems and examines others, applying the properties. Foundational work involves sets, mappings, and relations. The student gains experience reading and applying theorems, examining proofs for understanding, and constructing her own proofs.
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MT 347 - Modern Algebra
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MT 350: Differential Equations
4.00 Credits
Alverno College
Prereq. MT 253 - The student learns about differential equations as descriptions of changing phenomena. She studies solutions from several perspectives, surveying basic analytic methods for solving differential equations, learning to use graphical and qualitative approaches to analyze behavior of solutions, and using the computer to obtain numerical solutions. She works to interpret mathematical results in realistic contexts.
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MT 350 - Differential Equations
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MT 420: Axiomatic Systems
4.00 Credits
Alverno College
Prereq. MT 253 - The student learns about the structure and scope of mathematical axiom systems in the context of modern geometries. She expands her analytic-thinking and problem-solving abilities as she reads, understands, and writes mathematical theorems and their proofs.
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MT 420 - Axiomatic Systems
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MT 441: Introduction to Number Theory
2.00 - 4.00 Credits
Alverno College
Prereq. MT 243 or MT 253 - The student examines properties, structures, theorems, and proofs related to numbers. Topics include divisibility, prime numbers, factorization, congruences, and proof by induction.
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MT 441 - Introduction to Number Theory
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MT 442: Logic
2.00 - 4.00 Credits
Alverno College
Prereq. MT 221 - The student learns about deductive reasoning and rules of inference. Other topics such as switching theory may be examined.
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MT 442 - Logic
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MT 445: Advanced Topics in Mathematics For Elementary/ Middle School Teachers
3.00 Credits
Alverno College
Prereq. MT 123 or MT 243 - The mathematics education student develops an in-depth understanding in the area of algebraic thinking, with emphasis given to proportional reasoning. Other middle school mathematics topics, such as geometry in two and three dimensions and probability and statistics, may be studied. The historical development of the elementary and middle school curriculum is examined, with emphasis on the teaching, learning, and assessment processes highlighted in local, state, and national standards documents.
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MT 445 - Advanced Topics in Mathematics For Elementary/ Middle School Teachers
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MT 460: Introduction to Real Analysis
4.00 Credits
Alverno College
Prereq. MT 254 - In this course, the student studies functions of real variables from an advanced viewpoint. She examines the concepts of sequence, limit, continuity, and derivative in a mathematically rigorous setting. She gains experience in mathematical thinking and writing, developing an appreciation of the nature and role of mathematical proof.
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MT 460 - Introduction to Real Analysis
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