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MATHEMATICS

**L.MAT-091: Intermediate Algebra**
This course is designed to prepare the student for college-level (100-level) coursework in Mathematics. The course covers arithmetic, pre-algebra, and elementary and intermediate algebra, including linear equations and linear functions and applications, exponents, scientific notation, and elementary geometry. 4 credits.

**L.MAT-110: Mathematics for Elementary & Middle School Teachers I**
This course begins to develop the solid foundation in K-8 mathematics needed by future elementary and middle school teachers. Guided by the content areas listed in the NCTM’s Principles and Standards for School Mathematics, this course will focus on Numbers and Operations and patterns (under the Algebra standard). In addition, this course will introduce students to professional recommendations and state requirements for mathematics instruction and provide students with a global perspective on mathematics achievement. This course does not fulfill mathematical modeling general education requirements. Prerequisites: Three years of high school mathematics including one year of Algebra II or a grade of C- or better in L.MAT-091. 4 credits. Current or future education majors only.

**L.MAT-111: Mathematics for Elementary & Middle School Teachers II-FM**
This course provides further instruction on K-8 mathematics for prospective elementary and middle school teachers. MAT-111 focuses on the remaining three of the five NCTM content standards: Geometry, Measurement, and Probability, and continues to develop the Algebra standard. The course topics are taught using teaching techniques appropriate for elementary and middle school, including guided discovery and other student-centered approaches. This course satisfies the modeling with Mathematics requirement. Current or future education majors only. Prerequisite: L.MAT-110. 4 credits.

**L.MAT-113: College Algebra-FM**
Advanced work in algebra, functions and graphing in the context of mathematical models. Topics include linear, polynomial, exponential and logarithmic functions and regression. Prerequisite: Three years of high school mathematics including one year of Algebra II or a grade of C- or better in L.MAT-091. May not be taken for credit if a grade of C or higher was achieved in MAT-117 or a higher level mathematics course. 3 credits.

**L.MAT-115: Statistics-FM**
Basic statistical concepts and methods. Descriptive statistics and probability, distribution and sampling theory, hypothesis testing and analysis of variance, correlation and regression. Prerequisite: Three years of high school Mathematics including one year of Algebra II or a grade of C- or better in L.MAT-091. 4 credits.

**L.MAT-117: Pre-Calculus-FM**
This course provides a one semester preparation for Calculus while presenting an introduction to mathematical modeling. Topics include: linear, quadratic, exponential, and trigonometric models. Prerequisite: Four years of high school mathematics or permission of the instructor or L.MAT-113. 4 credits.

**L.MAT-124: Finite Mathematics: A Modeling Approach-FM**
Mathematics of linear and probabilistic models that assist in decision-making processes. Topics include linear programming and probability. Prerequisites: Four years of high school mathematics, or a grade of C- or better in L.MAT-113, or permission of instructor. 4 credits.

**L.MAT-150: Calculus of One Variable I-FM**
A study of the basic concepts and techniques of analytic geometry, differential and integral calculus of functions of one variable, and applications to calculus based models. Prerequisite: Demonstrated competency in L.MAT-113 and 117 or equivalent or superior high school mathematics background. May not be taken for credit if credit has previously been received for L.MAT-170. 4 credits.

**L.MAT-160: Calculus of One Variable II**
Further study of the integral calculus of functions of one variable and an introduction to sequences, series, and differential equations. Prerequisite: L.MAT-150 or equivalent. May not be taken for credit if credit has previously been received for L.MAT-170. 4 credits.

**L.MAT-170: Accelerated Calculus of One Variable-FM**
A course for students who have had one year of calculus in high school and are familiar with the computational aspects of the subject. Topics include functions, limits, continuity, derivatives, integrals, sequences, series, an introduction to differential equations, and an introduction to the modeling process. Upon completion of this course, students are prepared for Calculus III (L.MAT-260). Prerequisite: One year of high school calculus or permission of instructor.

**May not be taken for credit if credit has previously been received for L.MAT-150 or L.MAT-160**. 4 credits.

**L.MAT-220: Introduction to Probability & Statistics**
A study of the fundamental techniques used in descriptive statistics as applied to real-world data and the processes associated with the design and analysis of experiments; application of theories from Calculus to the construction of cumulative distributions for continuous random variables and computation of associated probabilities, expected values and variances. Prerequisite: L.MAT-150 or 170. 3 credits.

**L.MAT-230: Discrete Mathematics**
This course introduces the ideas and methods of logic and proofs. Topics include: set theory, logic, functions, proof types and elementary number theory. Prerequisite: L.MAT-150 and one of either L.MAT-160 or L.CIT-115 can be taken as a co-requisite, or L.MAT-170. 3 credits.

**L.MAT-250: Linear Algebra**
A course which introduces abstract vector spaces, matrices and linear transformations. Prerequisite: L.MAT-150 or L.MAT-170, or permission of the instructor. 3 credits.

**L.MAT-260: Analytic Geometry & Calculus III**
A study of partial differentiation and multiple integration, elementary vector analysis and applications of these concepts.. Prerequisite: L.MAT-160 or 170. 4 credits.

**L.MAT-310: Ordinary Differential Equations**
Theory, solution and applications of ordinary differential equations including Laplace transform methods. Prerequisite: L.MAT-160 or MAT-170. 3 credits.

**L.MAT-370: Numerical Analysis**
A study of some of the standard numerical algorithms used to solve real-world problems arising in engineering and the sciences, and use of a computer to implement these algorithms; pitfalls in computation, error analysis, solving linear systems, interpolation and approximation. Applies to a major in Mathematics or Computer Science, but not both. Prerequisites: L.MAT-160 or 170 and L.CIT-115. 3 credits.

**L.MAT-380: Modern Geometry**
Both Euclidean and non-Euclidean geometries are studied from an axiomatic viewpoint. Traditional high school geometry concepts are presented in a rigorous fashion so as to expand one's depth of understanding of traditional geometry. Prerequisite: L.MAT-230 or permission of the instructor. 3 credits.

**L.MAT-390: Mathematics Seminar**
A course where students experience and learn mathematics beyond that contained in usual coursework. Participants carry out research in an area of mathematics of interest to them with a faculty mentor. Each student gives at least one presentation on their topic and make definite progress toward the completion of the senior paper and presentation. Prerequisite: L.MAT-260, and 230; L.MAT-250 can be taken as a co-requisite. 1 credit (may be repeated).

**L.MAT-391: Guided Research**
A course where students experience and learn mathematics beyond that contained in usual coursework. Participants carry out research in an area of mathematics in a small group. Groups will give presentations and submit a final artifact. Prerequisite: L.MAT-230, L.MAT-250, and L.MAT-260. 3 credits.

**L.MAT-450: Modern Algebra**
A course which covers basic ideas on groups, rings, integral domains, fields, and polynomials over a field. Prerequisite: L.MAT- 230, and L.MAT-250 can be taken as a co-requisite or permission of instructor. 3 credits.

**L.MAT-460: Real Analysis**
Further work in Calculus, including the properties of the real number system, limits and continuity, differentiation and integration, sequences and series. Prerequisite: L.MAT-160 or 170, and L.MAT-230; L.MAT-250 can be taken as a co-requisite or permission of instructor. 3 credits.

**L.MAT-490: Math Portfolio-PJ**
Students will assemble a portfolio that provides evidence of appreciable growth in their understanding of mathematics, and reflect on the relevance of the Loras College Dispositions and lifelong learning skills to their development in the major and as a person. This course satisfies the General Education Portfolio requirement. Prerequisite: Declared Mathematics major, completion of three of the five advanced general education courses, L.MAT-230, 250, and 260, L.MAT-391 or at least two semesters of L.MAT-390. 1 credit.

**L.MAT-495: Topics in Mathematics**
Selected topics of current interest to students. Prerequisite: Permission of instructor. Credits arranged.

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