Department of Speech, Language and Hearing Sciences

# Bachelor of Science in Speech and Hearing Sciences

Students on Summer 2018, Fall 2018, or Spring 2019 requirements SLHSBS

The Bachelor of Science in Speech and Hearing Sciences provides a more scientific and mathematical background in the field. An undergraduate curriculum may be selected to provide a strong preparation for continued study at the graduate level in speech and hearing sciences.

## Requirements

The major requires at least 33 credit hours*, including the requirements listed below.

**Introductory Sequence.****Hearing Science: An Overview.**One (1) course:- SLHS-S 106 Hearing Science: An Overview

# SLHS-S 106 Hearing Science: An Overview

- Credits
- 3
- Prerequisites
- None
- Description
- Introduction to hearing science and how it is applied toward the evaluation and treatment of clinical problems.
- Repeatability
- Credit given for only one of SLHS-S 106 or SPHS-S 106.

**Speech and Language Sciences: An Overview.**One (1) course:- SLHS-S 108 Speech and Language Sciences: An Overview

# SLHS-S 108 Speech and Language Sciences: An Overview

- Credits
- 3
- Prerequisites
- None
- Description
- Introduction to the development and use of speech and language across the lifespan and to the scientific foundations of typical spoken communication. Surveys the application of speech and language sciences to the understanding of some common disorders of speech and language.
- Repeatability
- Credit given for only one of SLHS-S 108 or SPHS-S 108.

**Core.****Introduction to Phonetics.**One (1) course:- SLHS-S 111 Introduction to Phonetics for Speech, Language and Hearing Sciences

# SLHS-S 111 Introduction to Phonetics for Speech, Language and Hearing Sciences

- Credits
- 3
- Prerequisites
- None
- Description
- Provides an introduction to the sounds of human language and the skills needed to describe speech sounds in the articulatory and acoustic domains and transcribe speech using the International Phonetic Alphabet (IPA), including both broad and narrow transcription.
- Repeatability
- Credit given for only one of SLHS-S 111 or SPHS-S 111.

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**Speech Anatomy and Physiology.**One (1) course:- SLHS-S 201 Speech Anatomy and Physiology

# SLHS-S 201 Speech Anatomy and Physiology

- Credits
- 3
- Prerequisites
- None
- Description
- Covers anatomy and physiology of the speech mechanism; contemporary views of speech physiology; subsystems of the speech mechanism - respiratory, laryngeal, and supraglottal - integrated with a model of speech production. Includes laboratory experiences.
- Repeatability
- Credit given for only one of SLHS-S 201 and SPHS-S 201.

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**Cognitive and Communicative Aspects of Aging.**One (1) course:- SLHS-S 307 Cognitive and Communicative Aspects of Aging

# SLHS-S 307 Cognitive and Communicative Aspects of Aging

- Credits
- 3
- Prerequisites
- SLHS-S 104, SLHS-S 108, or SPHS-S 108; and SLHS-S 201, SPHS-S 201, or ANAT-A 215
- Description
- Review of cognitive and communicative changes associated with normal aging as well as with diseases and conditions that are prevalent in the aging population. Includes discussion of methodological issues in research on aging as well as principles for maximizing communication with the elderly population.
- Repeatability
- Credit given for only one of SLHS-S 307 or SPHS-S 307.

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**Introduction to Research in Speech, Language, and Hearing Sciences.**One (1) course:- SLHS-S 311 Introduction to Research in Speech, Language, and Hearing Sciences
- PSY-P 211 Methods of Experimental Psychology (with departmental approval)

# SLHS-S 311 Introduction to Research in Speech, Language, and Hearing Sciences

- Credits
- 3
- Prerequisites
- PSY-K 300 or STAT-S 303
- Description
- Introduction to research methodology in speech and hearing science, both basic and applied. Focuses on basic designs, analyses, and how research informs clinical practice. Course includes discussion of ethics, evaluation of research, and scientific writing.
- Repeatability
- Credit given for only one of SLHS-S 311 or SPHS-S 311.

# PSY-P 211 Methods of Experimental Psychology

- Credits
- 3
- Prerequisites
- PSY-P 101 or PSY-P 155
- Description
- Design and execution of simple experiments, treatment of results, search of the literature, and preparation of experimental reports.

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**Childhood Language.**One (1) course:- SLHS-S 333 Childhood Language

# SLHS-S 333 Childhood Language

- Credits
- 3
- Prerequisites
- At least sophomore standing
- Description
- Develops knowledge of how language is acquired by young children, examines data on what young infants and young children know about language at different ages, and considers the kinds of theories that may explain this data.
- Repeatability
- Credit given for only one of SLHS-S 333 or SPHS-S 333.

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**Speech Science.**One (1) course:- SLHS-S 350 Speech Science

# SLHS-S 350 Speech Science

- Credits
- 3
- Prerequisites
- At least sophomore standing; and SLHS-S 104, SLHS-S 108, or SPHS-S 108; and SLHS-S 201 or SPHS-S 201
- Description
- Provides an overview of speech production, including acoustics and physiology, as well as speech perception. The focus is on non-disordered speech in adults with some coverage of development as warranted.
- Repeatability
- Credit given for only one of SLHS-S 350 or SPHS-S 350.

**Hearing Science.**One (1) course:- SLHS-S 375 Hearing Science

# SLHS-S 375 Hearing Science

- Credits
- 3
- Prerequisites
- At least sophomore standing; and SLHS-S 104, SLHS-S 106, or SPHS-S 106
- Description
- Provides an in-depth study of hearing in the normal auditory system. Topics include anatomy and physiology of the ear, anatomy and physiology of the auditory brain, and auditory perception and psychophysics.
- Repeatability
- Credit given for only one of SLHS-S 375 or SPHS-S 375.

**Advanced.**Complete two (2) different courses (Note: selecting a different topic of the same course will not fulfill this requirement) selected from the Topical Seminar list.- SLHS-S 423 Topical Seminar in Speech, Language and Hearing Sciences
- SLHS-S 425 Topical Seminar in Speech Science
- SLHS-S 427 Topical Seminar in Language Sciences
- SLHS-S 429 Topical Seminar in Hearing Science
- SLHS-S 470 Assessment and Treatment of Hearing Loss

# SLHS-S 423 Topical Seminar in Speech, Language and Hearing Sciences

- Credits
- 3
- Prerequisites
- At least junior standing
- Description
- In-depth study of specific topics in speech science, language science, and hearing science. Topics vary by semester.
- Repeatability
- May be repeated with different topics for a maximum of 9 credit hours.

# SLHS-S 425 Topical Seminar in Speech Science

- Credits
- 3
- Prerequisites
- At least junior standing; and SLHS-S 350 or SPHS-S 350
- Description
- In-depth study of specific topics in speech science. Topics vary by semester.
- Repeatability
- May be repeated with a different topic for a maximum of 9 credit hours in SLHS-S 425 and SPHS-S 425.

# SLHS-S 427 Topical Seminar in Language Sciences

- Credits
- 3
- Prerequisites
- At least junior standing; and SLHS-S 333 or SPHS-S 333
- Description
- In-depth study of specific topics in language science. Topics vary by semester.
- Repeatability
- May be repeated with different topics for a maximum of 9 credit hours in SLHS-S 427 or SPHS-S 427.

# SLHS-S 429 Topical Seminar in Hearing Science

- Credits
- 3
- Prerequisites
- At least junior standing; and SLHS-S 375 or SPHS-S 375
- Description
- In-depth study of specific topics in hearing science. Topics vary by semester.
- Repeatability
- May be repeated with different topics for a maximum of 9 credit hours in SLHS-S 429 and SPHS-S 429.

# SLHS-S 470 Assessment and Treatment of Hearing Loss

- Credits
- 3
- Prerequisites
- At least junior standing; and SLHS-S 375 or SPHS-S 375
- Description
- Covers basic acoustics, anatomy and physiology of the auditory system with a focus on the applied principles of audiologic evaluation, management, and (re)habilitation options for adult and pediatric populations. It is geared toward upper-level undergraduate students majoring in speech, language, and hearing sciences.

**Addenda requirements**.****Psychology.**One (1) course:- PSY-P 101 Introductory Psychology I
- PSY-P 155 Introduction to Psychological and Brain Sciences

# PSY-P 101 Introductory Psychology I

- Credits
- 3
- Prerequisites
- None
- Description
- Introduction to psychology; its methods, data, and theoretical interpretations in areas of learning, sensory psychology, and psychophysiology.
- Repeatability
- Credit given for only one of PSY-P 101, PSY-P 106, PSY-P 151, or PSY-P 155. Equivalent to IUPUI PSY-B 105 and PSY-P 151.

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# PSY-P 155 Introduction to Psychological and Brain Sciences

- Credits
- 3
- Prerequisites
- None
- Description
- An introduction to psychological and brain sciences for psychology majors. Introduces students to the history of psychology and its place in science, to the experimental method, and to the broad range of topics studied by psychological scientists.
- Repeatability
- Credit given for only one of PSY-P 101, PSY-P 106, PSY-P 151, or PSY-P 155.

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**Linguistics.**One (1) course:- LING-L 103 Introduction to the Study of Language
- LING-L 203 Introduction to Linguistic Analysis

# LING-L 103 Introduction to the Study of Language

- Credits
- 3
- Prerequisites
- None
- Description
- A survey of perspectives on language, covering topics such as the relation between the form of words and sentences and their meanings, the sounds of languages and their dialect variations, the use of language in daily life, language in humans and animals, and the relationship between language and thought.

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# LING-L 203 Introduction to Linguistic Analysis

- Credits
- 3
- Prerequisites
- None
- Description
- Introduction to basic concepts of linguistic analysis, exemplifying the general principles of structural approaches to the modeling of language. Focus on, and application of, analytical methods applied in phonetics/phonology and morphology/syntax.
- Repeatability
- Credit given for only one of LING-L 203 or LING-L 303.

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**Statistics.**One (1) course:- STAT-S 303 Applied Statistical Methods for the Life Sciences
- PSY-K 300 Statistical Techniques

# STAT-S 303 Applied Statistical Methods for the Life Sciences

- Credits
- 3
- Prerequisites
- None
- Notes
- R: Mastery of high school algebra; or MATH-M 014
- Description
- Introduction to methods for analyzing data arising in the life sciences, designed for biology, human biology, and pre-medical students. Graphical and numerical descriptions of data, probability models, fundamental principles of estimation and hypothesis testing, inferences about means, correlation, linear regression.
- Repeatability
- Credit given for only one of ANTH-A 306, CJUS-K 300, ECON-E 370, ECON-S 370, MATH-K 300, MATH-K 310, POLS-Y 395, PSY-K 300, PSY-K 310, SOC-S 371, SPEA-K 300, SPH-Q 381, STAT-K 310, STAT-S 300, STAT-S 301, or STAT-S 303.

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# PSY-K 300 Statistical Techniques

- Credits
- 3
- Prerequisites
- One of MATH-M 106, MATH-M 118, MATH-M 119, MATH-M 211, MATH-M 212, MATH-S 211, MATH-S 212, MATH-V 118, or, MATH-V 119
- Description
- Introduction to statistics; nature of statistical data; ordering and manipulation of data; measures of central tendency and dispersion; elementary probability. Concepts of statistical inference and decision: estimation and hypothesis testing. Special topics include regression and correlation, analysis of variance, non-parametric methods.
- Repeatability
- Credit given for only one of ANTH-A 306, CJUS-K 300, ECON-E 370, ECON-S 370, MATH-K 300, MATH-K 310, POLS-Y 395, PSY-K 300, PSY-K 310, SOC-S 371, SPEA-K 300, SPH-Q 381, STAT-K 310, STAT-S 300, STAT-S 301, or STAT-S 303.

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**Biology.**One (1) course:- 3 credit hours in biology
- ANAT-A 215 BASIC HUMAN ANATOMY
- PHSL-P 215 BASIC HUMAN PHYSIOLOGY

# ANAT-A 215 BASIC HUMAN ANATOMY

- Credits
- 3–5 credit hours
- Prerequisites
- None
- Description
- None

# PHSL-P 215 BASIC HUMAN PHYSIOLOGY

- Credits
- 4–5 credit hours
- Prerequisites
- None
- Description
- None

**Physics.**One (1) course:- PHYS-P 105 Basic Physics of Sound

# PHYS-P 105 Basic Physics of Sound

- Credits
- 3
- Prerequisites
- None
- Description
- Physical principles involved in the description, generation, and reproduction of sound. Topics include physics of vibrations and waves, propagation, Fourier decomposition of complex wave forms, harmonic spectra, standing waves and resonance, sound loudness and decibels, room acoustics, analog/digital recording/ reproduction. For interested students, PHYS-P 109 is an optional companion laboratory course.

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**Mathematics.**- One (1) course:
- Both of the following:
- MATH-D 116 Introduction to Finite Mathematics I
- MATH-D 117 Introduction to Finite Mathematics II

- MATH-M 118 Finite Mathematics
- MATH-S 118 Honors Finite Mathematics
- MATH-V 118 Finite Mathematics with Applications

# MATH-D 116 Introduction to Finite Mathematics I

- Credits
- 2
- Prerequisites
- Mastery of two years of high school algebra as indicated by an ALEKS score of 40 or higher; or MATH-M 014, MATH-M 018, or MATH-J 111.
- Description
- MATH-D 116 and MATH-D 117 is a two-course sequence that covers sets, counting, basic probability, including random variables and expected values, linear systems, matrices, linear programming, and applications.
- Repeatability
- Credit given for only one of MATH-A 118, MATH-M 118, MATH-S 118, MATH-V 118; or MATH-D 116 and MATH-D 117.

# MATH-D 117 Introduction to Finite Mathematics II

- Credits
- 2
- Prerequisites
- MATH-D 116 or consent of the department
- Notes
- MATH-D 116 and MATH-D 117 is a two-course sequence
- Description
- Topics for the course are taken from MATH-M 118. Credit for the College of Arts and Sciences Foundations requirement in Mathematical Modeling or the College's N&M Breadth of Inquiry requirement will be given only upon completion of both MATH-D 116 and MATH-D 117 with a passing grade.
- Repeatability
- Credit given for only one of MATH-A 118, MATH-M 118, MATH-S 118, MATH-V 118; or MATH-D 116 and MATH-D 117.

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# MATH-M 118 Finite Mathematics

- Credits
- 3
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra as indicated by an appropriate ALEKS score or completion of MATH-M 014, MATH-M 018, or MATH-J 111
- Description
- Sets, counting, basic probability, including random variables and expected values. Linear systems, matrices, linear programming, and applications.
- Repeatability
- Credit given for only one of MATH-A 118, MATH-M 118, MATH-S 118, MATH-V 118; or MATH-D 116 and MATH-D 117.

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# MATH-S 118 Honors Finite Mathematics

- Credits
- 3
- Prerequisites
- Hutton Honors College membership
- Notes
- R: To be successful students will demonstrate mastery of two years of high school algebra as indicated by an appropriate ALEKS score or completion of MATH-M 014, MATH-M 018, or MATH-J 111
- Description
- Designed for students of outstanding ability in mathematics. Covers all material of MATH-M 118 and additional topics from statistics and game theory. Computers may be used in this course, but no previous experience is assumed.

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# MATH-V 118 Finite Mathematics with Applications

- Credits
- 3
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra as indicated by an appropriate ALEKS score or completion of MATH-M 014, MATH-M 018, or MATH-J 111
- Description
- Sets, counting, basic probability, linear modelling, and other discrete topics. Applications to various areas depending on topic. Possibilities include social and biological sciences and consumer mathematics.
- Repeatability

- Fall 2023CASE NMcourse

- Both of the following:
- One (1) course:
- MATH-J 113 Introduction to Calculus with Applications
- MATH-M 119 Brief Survey of Calculus I
- MATH-M 120 Brief Survey of Calculus II
- MATH-M 211 Calculus I
- MATH-M 212 Calculus II
- MATH-M 247 Mathematical Contest in Modeling Preparation
- MATH-M 298 Careers in Mathematics
- MATH-M 301 Linear Algebra and Applications
- MATH-M 303 Linear Algebra for Undergraduates
- MATH-M 311 Calculus III
- MATH-M 312 Calculus IV
- MATH-M 321 Intuitive Topology
- MATH-M 330 Exploring Mathematical Ideas
- MATH-M 343 Introduction to Differential Equations with Applications I
- MATH-M 344 Introduction to Differential Equations with Applications II
- MATH-M 348 Discrete Mathematical Models
- MATH-M 353 Discrete Mathematics
- MATH-M 365 Introduction to Probability and Statistics
- MATH-M 371 Elementary Computational Methods
- MATH-M 380 History of Mathematics
- MATH-M 384 Logic
- MATH-M 385 Mathematics from Language
- MATH-M 391 Introduction to Mathematical Reasoning
- MATH-M 403 Introduction to Modern Algebra I
- MATH-M 404 Introduction to Modern Algebra II
- MATH-M 405 Number Theory
- MATH-M 409 Linear Transformations
- MATH-M 413 Introduction to Analysis I
- MATH-M 414 Introduction to Analysis II
- MATH-M 415 Elementary Complex Variables with Applications
- MATH-M 420 Metric Space Topology
- MATH-M 435 Introduction to Differential Geometry
- MATH-M 436 Introduction to Geometries
- MATH-M 441 Introduction to Partial Differential Equations with Applications I
- MATH-M 442 Introduction to Partial Differential Equations with Applications II
- MATH-M 447 Mathematical Models and Applications I
- MATH-M 451 The Mathematics of Finance
- MATH-M 453 Cryptography
- MATH-M 463 Introduction to Probability Theory I
- MATH-M 464 Introduction to Probability Theory II
- MATH-M 466 Introduction to Mathematical Statistics
- MATH-M 471 Numerical Analysis I
- MATH-M 472 Numerical Analysis II
- MATH-M 482 Modal Logic
- MATH-M 490 Problem Seminar
- MATH-M 491 Putnam Exam Seminar

# MATH-J 113 Introduction to Calculus with Applications

- Credits
- 3
- Prerequisites
- MATH-J 112 with a grade of C- or higher; or consent of department
- Notes
- For Groups students only. MATH-J 113 can count toward the College of Arts and Sciences Foundations requirement in mathematical modeling and the College of Arts and Sciences natural and mathematical sciences Breadth of Inquiry requirement for Groups studentsï»¿
- Description
- A survey of calculus.
- Repeatability
- Credit given for only one of MATH-J 113, MATH-M 119, MATH-V 119, MATH-M 211, or MATH-S 211.

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# MATH-M 119 Brief Survey of Calculus I

- Credits
- 3
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra, one year of high school geometry, and pre-calculus as indicated by an appropriate ALEKS score or completion of MATH-M 025 or MATH-M 027
- Description
- Introduction to calculus. Primarily for students from business and the social sciences.
- Repeatability
- Credit given for only one of MATH-J 113, MATH-M 119, MATH-V 119, MATH-M 211, or MATH-S 211.

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# MATH-M 120 Brief Survey of Calculus II

- Credits
- 3
- Prerequisites
- MATH-M 119 or MATH-V 119
- Description
- A continuation of MATH-M 119 covering topics in elementary differential equations, calculus of functions of several variables and infinite series. Intended for non-physical science students.
- Repeatability
- Credit given for only one of MATH-M 120 or MATH-M 212.

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# MATH-M 211 Calculus I

- Credits
- 4
- Prerequisites
- None
- Notes
- R: To be successful, students will demonstrate mastery of two years of high school algebra, one year of high school geometry, and pre-calculus, and trigonometry as indicated by an appropriate ALEKS score or completion of MATH-M 027
- Description
- Limits, continuity, derivatives, definite and indefinite integrals, applications.
- Repeatability
- A student may receive credit for only one of the following: MATH-J 113, MATH-M 119, MATH-V 119, MATH-M 211, or MATH-S 211.

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# MATH-M 212 Calculus II

- Credits
- 4
- Prerequisites
- MATH-M 211 or MATH-S 211; or consent of department
- Description
- Techniques of integration (by parts, trigonometric substitutions, partial fractions), improper integrals, volume, work, arc length, surface area, infinite series.
- Repeatability
- Credit given for only one of MATH-M 120 or MATH-M 212.

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# MATH-M 247 Mathematical Contest in Modeling Preparation

- Credits
- 1
- Prerequisites
- None
- Description
- Trains students for the Mathematical Contest in Modeling (MCM) through the preparation of solutions to two past MCM problems. MCM is an annual contest where teams of undergraduates use mathematical modeling to present their solutions to real world problems.
- Repeatability
- May be repeated for a maximum of 3 credit hours.

# MATH-M 298 Careers in Mathematics

- Credits
- 1
- Prerequisites
- None
- Notes
- R: Sophomore or junior standing
- Description
- Invited speakers provide perspectives from a variety of fields. Helps match student skills and interests to the requirements of a chosen career. How to use campus career development resources, write a resume and cover letter, and develop interviewing and networking skills for the job market. Options to prepare for professional or graduate education.

# MATH-M 301 Linear Algebra and Applications

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212; or MATH-M 211 and CSCI-C 241; or MATH-S 211 and CSCI-C 241
- Description
- Solving systems of linear equations, matrix algebra, determinants, vector spaces, eigenvalues and eigenvectors. Selection of advanced topics. Applications throughout. Computer used for theory and applications.
- Repeatability
- Credit given for only one of MATH-M 301 or MATH-M 303.

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# MATH-M 303 Linear Algebra for Undergraduates

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212; or MATH-M 211 and CSCI-C 241; or MATH-S 211 and CSCI-C 241
- Description
- Introduction to the theory of real vector spaces. Coordinate s, linear dependence, bases. Linear transformations and matrix calculus. Determinants and rank. Eigenvalues and eigenvectors.
- Repeatability
- Credit given for only one of MATH-M 301, MATH-M 303, or MATH-S 303.

- Fall 2023CASE NMcourse

# MATH-M 311 Calculus III

- Credits
- 4
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Elementary geometry of 2, 3, and n-space; functions of several variables; partial differentiation; minimum and maximum problems; multiple integration.

- Fall 2023CASE NMcourse

# MATH-M 312 Calculus IV

- Credits
- 3
- Prerequisites
- MATH-M 311 or MATH-S 311
- Description
- Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. Vector integral calculus: line integrals, Green\'s theorem, surface integrals, Stokes\' theorem. Applications.
- Repeatability
- Credit given for only one of MATH-M 312 or MATH-S 312.

# MATH-M 321 Intuitive Topology

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Intuitive description of topology, including networks and maps, topological equivalence, classification of surfaces, spheres with handles, knot theory, Jordan curve theorem, transformations, and fixed-point theorems.

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# MATH-M 330 Exploring Mathematical Ideas

- Credits
- 3
- Prerequisites
- MATH-M 211 or MATH-S 211
- Notes
- Does not count toward major requirements
- Description
- An experimental course to illustrate important ideas in major areas of mathematics, including number theory, group theory, topology, geometry, and probability. Additional topics may include newly emerging fields, such as chaos theory.

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# MATH-M 343 Introduction to Differential Equations with Applications I

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Notes
- R: MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Ordinary differential equations and methods for their solution, including series methods and the Laplace transform. Applications of differential equations. s, stability, and numerical methods. Partial differential equations of mathematical physics, Fourier series.
- Repeatability
- Credit given for only one of MATH-M 343 or MATH-S 343.

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# MATH-M 344 Introduction to Differential Equations with Applications II

- Credits
- 3
- Prerequisites
- One of MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 343 or MATH-S 343
- Description
- Ordinary differential equations and methods for their solution, including series methods and the Laplace transform.Â Applications of differential equations.Â Systems, stability, and numerical methods.Â Partial differential equations of mathematical physics, Fourier series.

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# MATH-M 348 Discrete Mathematical Models

- Credits
- 3
- Prerequisites
- MATH-M 118 or equivalent
- Description
- Introduction to the development and use of discrete mathematical models in the social, life, and management sciences; emphasis on models involving Markov chains, game theory, graph theory, and evolutionary systems.

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# MATH-M 353 Discrete Mathematics

- Credits
- 3
- Prerequisites
- MATH-M 212 or consent of instructor
- Description
- Covers fundamental topics chosen from enumerative combinatorics and graph theory. Possible topics include permutations, combinations, pigeonhole principle, inclusion-exclusion, generating functions, recurrence relations, PÃ³lya theory, spanning trees, Eulerian paths, Ramsey theory, graph coloring, flow problems, Hamiltonian paths and cycles, electrical networks, random graphs.

# MATH-M 365 Introduction to Probability and Statistics

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Elementary concepts of probability and statistics. Combinatorics, conditional probability, independence, random variables, discrete and continuous distributions, moments. Statistical inference, point estimation, confidence intervals, test of hypotheses. Applications to social, behavioral, and natural sciences.
- Repeatability
- Credit given for only one of MATH-M 360 or MATH-M 365.

- Fall 2023CASE NMcourse

# MATH-M 371 Elementary Computational Methods

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Interpolation and approximation of functions, solution of equations, numerical integration and differentiation. Errors, convergence, and stability of the procedures. Students write and use programs applying numerical methods.

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# MATH-M 380 History of Mathematics

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Brief study of the development of algebra and trigonometry; practical, demonstrative, and analytic geometry; calculus, famous problems, calculating devices; famous mathematicians and chronological outlines in comparison with outlines in the sciences, history, philosophy, and astronomy.
- Repeatability
- Credit given for only one of HPSC-X 380 or MATH-M 380.

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# MATH-M 384 Logic

- Credits
- 3
- Prerequisites
- CSCI-C 241, MATH-M 303, or MATH-S 303
- Description
- Construction and study of formal mathematical languages. Definitions of, and relationships between, the notions of truth and provability of a formal sentence. Proof systems for logical systems such as propositional logic and syllogistic logic. Soundness, completeness, and decidability.

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# MATH-M 385 Mathematics from Language

- Credits
- 3
- Prerequisites
- MATH-M 118, MATH-S 118, or equivalent
- Description
- Discrete mathematics. Topics in math motivated by linguistics, chosen from formal approaches to syntax and semantics, and from statistical and computational linguistics.

- Fall 2023CASE NMcourse

# MATH-M 391 Introduction to Mathematical Reasoning

- Credits
- 3
- Prerequisites
- (A) MATH-M 212, MATH-M 213, or MATH-S 212; or CSCI-C 241 and MATH-M 211; or CSCI-C 241 and MATH-S 211; and (B) MATH-M 301, MATH-M 303, or MATH-S 303
- Notes
- Recommended for students with insufficient background for 400-level courses and for students in education
- Description
- Elementary logic, techniques of proof, basic set theory, functions, relations, binary operations, number systems, counting. Bridges the gap between elementary and advanced courses.
- Repeatability
- Not open to students who have received credit for MATH-M 403, MATH-M 413, or MATH-M 420.

- Fall 2023CASE NMcourse

# MATH-M 403 Introduction to Modern Algebra I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Study of groups, rings, field extensions, with applications to linear transformations.

# MATH-M 404 Introduction to Modern Algebra II

- Credits
- 3
- Prerequisites
- None
- Notes
- Open only to graduate students
- Description
- Study of groups, rings, field extensions, with applications to linear transformations.

# MATH-M 405 Number Theory

- Credits
- 3
- Prerequisites
- MATH-M 212, MATH-M 213, or MATH-S 212
- Description
- Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruences, primitive roots, diophantine equations, quadratic residues, sums of squares.

# MATH-M 409 Linear Transformations

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- The study of linear transformations on a finite dimensional vector space over the complex field. Canonical forms, similarity theory; inner products and diagonalization of normal transformations.

# MATH-M 413 Introduction to Analysis I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
- Description
- Modern theory of real number , limits, functions, sequences and series, Riemann-Stieltjes integral, and special topics.

# MATH-M 414 Introduction to Analysis II

- Credits
- 3
- Prerequisites
- MATH-M 413 or MATH-S 413
- Description
- Continuation of MATH-M 413. Functions of several variables, Taylor series, extreme values. Manifolds in Euclidean space, Implicit Function Theorem, Inverse Function Theorem. Divergence Theorem and other classical theorems of vector calculus. Special topics.
- Repeatability
- Credit given for only one of MATH-M 414 or MATH-S 414.

# MATH-M 415 Elementary Complex Variables with Applications

- Credits
- 3
- Prerequisites
- MATH-M 311, MATH-S 311, or consent of instructor
- Description
- Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, integrations, calculus of residues, conformal mapping. Application to physics.
- Repeatability
- Credit given for only one of MATH-M 415 or MATH-S 415.

# MATH-M 420 Metric Space Topology

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Topology of Euclidean and metric spaces. Limits and continuity. Topological properties of metric spaces, including separation properties, connectedness, and compactness. Complete metric spaces. Elementary general topology.

# MATH-M 435 Introduction to Differential Geometry

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
- Description
- An introduction to the geometry of curves and surfaces. Topics will include arc length, torsion, Frenet formulae, metrics, curvatures, and classical theorems in these areas.

# MATH-M 436 Introduction to Geometries

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- Non-Euclidean geometry, axiom systems. Plane projective geometry, Desarguesian planes, perspectivities, coordinates in the real projective plane. The group of projective transformations and subgeometries corresponding to subgroups. Models for geometries. Circular transformations.

# MATH-M 441 Introduction to Partial Differential Equations with Applications I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311; and MATH-M 343 or MATH-S 343
- Notes
- R: MATH-M 312 or MATH-S 312
- Description
- Derivation and methods of solution of classical partial differential equations of mathematical physics: heat, wave, and Laplace equations. Separation of variables, Fourier series, Sturm-Liouville theory, special functions, Green\'s functions, Fourier transform, first order equations, characteristics and special topics.

# MATH-M 442 Introduction to Partial Differential Equations with Applications II

- Credits
- 3
- Prerequisites
- MATH-M 441
- Description
- Derivation and methods of solution of classical partial differential equations of mathematical physics: heat, wave, and Laplace equations. Separation of variables, Fourier series, Sturm-Liouville theory, special functions, Green\'s functions, Fourier transform, first order equations, characteristics and special topics.

# MATH-M 447 Mathematical Models and Applications I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
- Notes
- P or C: MATH-M 365
- Description
- Formation and study of mathematical models used in the biological, social, and management sciences. Mathematical topics include games, graphs, Markov and Poisson processes, mathematical programming, queues, and equations of growth.

# MATH-M 451 The Mathematics of Finance

- Credits
- 3
- Prerequisites
- MATH-M 311 or MATH-S 311; and MATH-M 365 or MATH-M 463 or MATH-S 463
- Description
- Course covers probability theory, Brownian motion, Ito\'s Lemma, stochastic differential equations, and dynamic hedging. These topics are applied to the Black-Scholes formula, the pricing of financial derivatives, and the term theory of interest rates.

# MATH-M 453 Cryptography

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303
- Description
- The course covers encryption and decryption in secure codes. Topics include cryptos and their cryptanalysis, Data Encryption Standard, cryptanalysis, Euclidean algorithm, Chinese remainder theorem, RSA crypto, primality testing, factoring algorithms, EI Gamal crypto, discrete log problem, other public key cryptos, signature schemes, hash functions, key distribution and key agreement.

- Fall 2023CASE NMcourse

# MATH-M 463 Introduction to Probability Theory I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311
- Description
- The meaning of probability. Random experiments, conditional probability, independence. Random variables, expected values and standard deviations, moment generating functions. Important discrete and continuous distributions. Poisson processes. Multivariate distributions, basic limit laws such as the central limit theorem.
- Repeatability
- Credit given for only one of MATH-M 463 or MATH-S 463.

# MATH-M 464 Introduction to Probability Theory II

- Credits
- 3
- Prerequisites
- MATH-M 463 or MATH-S 463
- Description
- Conditional distributions and expectation, linear and nonlinear regression; simple stochastic processes: Poisson process, process with independent increments, random walk, Markov chain with finite state space; information theory.

# MATH-M 466 Introduction to Mathematical Statistics

- Credits
- 3
- Prerequisites
- MATH-M 463, MATH-S 463, or consent of instructor
- Description
- Rigorous mathematical treatment of problems in sampling and statistical inference. Method of maximum likelihood, efficiency, sufficient statistics, exponential family distributions, likelihood ratio tests, most powerful tests, minimum variance unbiased estimators, shortest confidence intervals, linear models and analysis of variance, nonparametric methods.

# MATH-M 471 Numerical Analysis I

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311; and MATH-M 343 or MATH-S 343
- Notes
- Knowledge of a computer language such as FORTRAN, C, C++, etc., is essential for success in this course. Students with other programming backgrounds should consult the instructor
- Description
- Interpolation and approximation of functions, numerical integration and differentiation, solution of nonlinear equations, acceleration and extrapolation, solution of systems of linear equations, eigenvalue problems, initial and boundary value problems for ordinary differential equations, and computer programs applying these numerical methods.

# MATH-M 472 Numerical Analysis II

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303, or MATH-S 303; and MATH-M 311 or MATH-S 311; and MATH-M 343 or MATH-S 343
- Notes
- Knowledge of a computer language such as FORTRAN, C, C++, etc., is essential for success in this course. Students with other programming backgrounds should consult the instructor.
- Description
- Interpolation and approximation of functions, numerical integration and differentiation, solution of nonlinear equations, acceleration and extrapolation, solution of s of linear equations, eigenvalue problems, initial and boundary value problems for ordinary differential equations, and computer programs applying these numerical methods.

# MATH-M 482 Modal Logic

- Credits
- 3
- Prerequisites
- CSCI-C 241, CSCI-H 241, MATH-M 303, MATH-S 303, or MATH-M 384; or consent of instructor
- Description
- Introduction to modal logic with emphasis on systems of modal logic which apply to philosophy and computer science. Includes epistemic logic, temporal logic, deontic logic, and logics for reasoning about space. Covers primarily the semantics of these systems, and secondarily the standard results about them.

- Fall 2023CASE NMcourse

# MATH-M 490 Problem Seminar

- Credits
- 3
- Prerequisites
- MATH-M 301, MATH-M 303 or MATH-S 303; and consent of instructor
- Notes
- R: MATH-M 343 or MATH-S 343, and MATH-M 441; and MATH-M 471
- Description
- Introduction to research techniques for advanced undergraduate and beginning graduate students, based on problems from parts of the regular curriculum, such as linear algebra, topology, probability, and analysis. Emphasis will be on problems of both current and historical interest but usually not in the standard literature.

# MATH-M 491 Putnam Exam Seminar

- Credits
- 1
- Prerequisites
- Consent of the director of undergraduate studies
- Description
- The Putnam Examination is a national mathematics competition for college undergraduates at all levels of study. It is held in December each year. This problem seminar is designed to help students prepare for the examination.
- Repeatability
- May be repeated for a maximum of 3 credit hours.

- Six (6) additional credit hours in mathematics

- One (1) course:

**Major GPA, Hours, and Minimum Grade Requirements.**- At least 18 credit hours in the major must be completed in courses taken through the Indiana University Bloomington campus or an IU-administered or IU co-sponsored Overseas Study program.
- At least 18 credit hours in the major must be completed at the 300–499 level.
- Except for the GPA requirement, a grade of C- or higher is required for a course to count toward a requirement in the major.
- A GPA of at least 2.000 for all courses taken in the major—including those where a grade lower than C- is earned—is required.
- Exceptions to major requirements may be made with the approval of the department's Director of Undergraduate Studies, subject to final approval by the College of Arts and Sciences.

Notes

The Bachelor of Science degree requires at least 120 credit hours, to include the following:

**College of Arts and Sciences Credit Hours.**At least 100 credit hours must come from College of Arts and Sciences disciplines.**Upper Division Courses.**At least 36 credit hours (of the 120) must be at the 300–499 level.**College Residency.**Following completion of the 60th credit hour toward degree, at least 36 credit hours of College of Arts and Sciences coursework must be completed through the Indiana University Bloomington campus or an IU-administered or IU co-sponsored Overseas Study program.**College GPA.**A cumulative grade point average (GPA) of at least 2.000 is required for all courses taken at Indiana University.**CASE Requirements.**The following College of Arts and Sciences Education (CASE) requirements must be completed:- CASE Foundations
- CASE Breadth of Inquiry
- CASE Culture Studies
- Diversity in the United States: Not required
- Global Civilizations and Cultures: Not required

- CASE Critical Approaches: 1 course
- CASE Foreign Language: Proficiency in a single foreign language through the first semester of the second year of college-level coursework
- CASE Intensive Writing: 1 course
- CASE Public Oral Communication: 1 course

**Major.**Completion of the major as outlined in the Major Requirements section above.

Most students must also successfully complete the Indiana University Bloomington General Education program.