History, theory, and practice of human and machine translation.

493. Readings in Linguistics. (l-3:0:Arr.) Blair

525. Descriptive Phonology. (3:3:0) Lytle

The structural description of the sound systems of language.

527. Descriptive Morphology. (3:3:0) Blair

The structural description of linguistic forms.

528. Syntax. (3:3:0) Prerequisite: Ling. 527. Lytle

Fundamental approach to generative grammar. Techniques of analysis

of linguistic data and preparation of grammatical statements through

ordered rules.

529R. Linguistic Structures. (3:3:1 ea.) Blair, Lytle

A consideration and comparison of the phonological and morphological

structures of several non-Indo-European languages. Students work with

native informants.

623. Problems in Contrastive Linguistics. (3:3:0) Bleiir

Contrast of structures in English and selected languages and the develop-

ment of grammatical description from these contrasts. Offered 1973 and

alternate years.

626. Problems in Historical Linguistics. (3:3:0) Lytle

Offered 1972 and alternate years.

693. Seminar in Linguistics. (2:2:0) Blair

Discussion of selected topics in linguistics.

699. Thesis for Master's Degree. (l-6:Arr.:0)

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MATHEMATICS 387

Mathematics

Professors: Burton, Feamley, Fletcher, Hillam (Chairman, 290 MSCB), Jamison,

Moore, Robinson, Yearout.

Associate Professors: Gee, Gill, Hansen, Higgins, Larsen, Olpin, Peterson, Skarda,

Snow, Wickes.

Assistant Professors: Armstrong, Campbell, Chatterley, Ferguson, Garner, Ham-

ilton, Haupt, Lamoreaux, Tolman, Walker, Walter, Wight, Wynn.

Instructor: Mouritsen.

The Mathematics Department offers courses leading toward the Bachelor of

Science and Master of Science degrees in mathematics and the Bachelor of Arts

and Master of Arts degrees in mathematics education.

Requirements for the Bachelor of Science Degree in Mathematics

An undergraduate student majoring in mathematics must present a program

prepared in consultation with an adviser appointed by the department. He must

complete his program with a grade average of C or better. The following are

required:

1. Math. 141, 142, 243. 244, 332, 371, 541, and either 372 or 542.

2. A minimum of 15 additional hours selected with prior approval of the de-

partment from Math. 372, 387, 411, 412, 434, 436, 451, 452, 501, 502, 508,

542. 551, 552.

In addition to the courses listed above, each departmental major is required

to pass a written comprehensive examination during the first semester of his

senior year.

Suggested Program: The following program is given as a guide in planning for

those who wish to major in mathematics:

Freshman Year F W P.E i i

Math. 141, 142 4 4 Dev. Assy I i

English 3 3 Electives 6 5

Relig. 121. 122 2 2

Health 130 2 Total hours 18 18

Hist. 170 3

If a student has not had adequate preparation in mathematics to permit

him to begin his college work at the level of analytic geometry and calculus, he

should substitute the necessary prerequisite courses for Math. 141 in the above

program. However, he should realize that as a consequence, additional time

will probably be required to complete all the requirements for graduation.

Majors in mathematics are encouraged to take advantage of the four hours

of religion credit that may be earned by attending the devotional assemblies

during each of the four years of the undergraduate program.

388 MATHEMATICS

In selecting courses to meet the physical science group requirement, a mathe-

matics major should consider only the following: Chem. 105, 106, or 111, 112;

Physics 121, 122, 221, 222, or 211, 213, 214.

All students who contemplate pursuing graduate work in mathematics are

urged to complete both Math. 372 and 542 and to gain competence in French,

German, or Russian while an undergraduate.

Requirements for the Bachelor of Arts Degree in Mathematics Education

An undergraduate major who wishes to teach mathematics in secondary schools

must present a program prepared in consultation with an adviser appointed

by the Mathematics Department. He must complete his program with a grade

average of C- or better. The following are required:

1. Math. 112, 113, and 214; or 141, 142, 243, and 244 or the equivalent.

2. Math. 301, 302, 371, and 451.

3. A minimum of nine semester hours selected from the following: Math. 210,

300, 332, 372, 385, 387, 411, 434, 452, 501, 502, 412, 541, 542, 551, 552.

4. A teaching minor as described in the Education section of this catalog.

In order to obtain the Bachelor of Arts degree in mathematics education, a

student must complete the teacher certification requirements outlined by the

Education Department.

Suggested Program: The following program is given as a guide in planning

for those who wish to major in mathematics education:

Freshman Year F W Hist. 170 3

Math. 112, 113 P.E i i

(or 141, 142) 4 4 Dev. Assy I i

English 3 3 Electives 6 5

Relig. 121, 122 2 2

Health 130 2 Total hours 18 18

If a student has not had adequate preparation in mathematics to permit him

to begin his college work at the level of analytic geometry and calculus, he

should substitute the necessary prerequisite courses for Math. 112 in the above

program. However, he should realize that as a consequence, additional time

will probably be required to complete all the requirements for graduation.

Undergraduate Minors

A student who majors in mathematics is not normally required to have a minor

but should work closely with an adviser to plan a program of elective courses

that meets his own educational objectives. A student who majors in mathe-

matics education, however, is required to have a teaching minor and should

consult the Education section of this catalog.

A student who wishes to minor in mathematics must complete with a grade

average of C- or better —

1. either of the sequences Math. 141, 142, 243; or Math. 112, 113, 214; and

2. a minimum of 9 additional credit hours in courses selected from the following:

Math. 244, 300, 332, 371, 372, 387, 411, 412, 434, 436, 451, 452, 501, 502,

508, 541, 542, 551. 552.

Graduate Degrees

The Department of Mathematics offers courses leading to the degrees of Master

of Science in mathematics and Master of Arts in mathematics education. Com-

plete details are available in the Graduate School Catalog.

Courses

90. Algebra. (0:3:0)

Equivalent to first year high school algebra.

MATHEMATICS 389

91. Plane Geometry, (0:3:0)

Equivalent to high school plane geometry.

97. Mathematical Review. (0:3:0) Prerequisite: Math. 111.

Review of mathematics through calculus. Primarily for returning

missionaries and others. Offered on the block plan.

101. Intermediate Algebra. (3:5:0) Home Study also. Prerequisites: Math.

90 and 91 or equivalent.

Equivalent to second year high school algebra.

105. College Algebra. (3:4:0) Home Study also. Prerequisite: Math. 101

or two years of high school algebra and one year of plane geometry.

Parallels part of Math. Ill at slower pace.

106. Trigonometry. (3:3:0) Home Study also. Prerequisite: Math. 105.

Parallels part of Math. Ill at slower pace.

108. Basic Analysis. (4:4:1) Prerequisite: Math. 101 or two years of high school

algebra.

Introduction to logic, matrix algebra, linear programming, and ele-

mentary functions. For students of business or social science.

109. Introduction to Calculus. (4:4:1) Prerequisite: Math. 108 or 111.

Introduction to plane analytic geometry and one-dimensional calculus.

Primarily for students in the colleges of Biological and Agricultural Sci-

ences and Business.

111. College Algebra and Trigonometry. (5:4:2) Home Study also. Prerequi-

sites: Math. 101 or two years of high school algebra and one year of plane

geometry.

112, 113. Analytic Geometry and Calculus I, 11. (4:4:0 ea.) Prerequisite: Math.

Ill or equivalent.

Plane analytic geometry; one-dimensional differential and integral calcu-

lus, with applications.

121, 122. Technical Mathematics. (3:2:3 ea.) Prerequisite: Math. 101.

College algebra, trigonometry, analytic geometry, and an introduction

to calculus. Problems and applications. Primarily for students in industrial

and technical education.

141, 142. Introduction to Calculus and Analysis. (4:4:0 ea.) Prerequisite: Math.

Ill or equivalent.

Plane analytic geometry and one-dimensional calculus, with applications.

Primarily for mathematics majors.

205H. Structure of Mathematics. (3:3:0)

Consideration of the structure and meaning of mathematics. For Honors

students who are taking no other mathematics courses.

210. Introduction to Mathematical Logic. (3:3:0) Prerequisite: Math. 105 or

111.

Traditional logic. Boolean algebra, algorithms, Turing machines.

214. Analytic Geometry and Calculus III. (3:3:0) Home Study also. Prerequi-

site: Math. 113.

Multidimensional calculus, infinite series.

223. Technical Mathematics. (3:3:0) Prerequisite: Math. 122.

Analytic geometry and calculus. Primarily for Technical Institute stu-

dents.

224. Numerical Methods in Technology. (3:3:0) Prerequisites: Math. 223 and

Comput. Sci. 231.

Interpolation, approximation, numerical differentiation and integration,

linear programming, solutions of equations. Primarily for students in in-

dustrial and technical education.

390 MATHEMATICS

243, 244. Intermediate Calculus and Analysis. (3:3:0 ea.) Prerequisite: Math.

142 or consent of department.

Multidimensional calculus.

291, 292. Honors Seminar in Mathematics. (1:1:0 ea.)

Seminar in structure of mathematics. Primarily for freshman and

sophomore mathematics majors. Open to other interested students.

300. History of Mathematics. (3:3:0) Home Study also. Prerequisite: Math.

112 or 301.

The development of mathematics, with emphasis on the underlying prin-

ciples and motivations.

301. Foundations of Algebra. (3:3:0) Prerequisites: Math. 106, 111, or 305.

Sets; logic; basic number systems. Required of prospective secondary

teachers.

302. Foundations of Geometry. (3:3:0) Prerequisite: Math. 112, 141, or 301.

The logical structure of Euclidean and non-Euclidean geometries. Re-

quired of prospective secondary teachers.

305. Basic Concepts of Mathematics, (3:3:0)

Designed to develop understanding of the basic structure of mathematics.

Required of and restricted to prospective elementary teachers.

306. Concepts of Mathematics. (3:3:0) Prerequisite: Math. 305.

Modular arithmetic; real numbers; complex numbers; relations and

functions; informal geometry. For elementary teachers.

307. Mathematics and the Humanities. (3:3:0) (G-ML)

Elementary ideas in contemporary mathematics for non-physical science

majors.

315. Methods of Advanced Calculus. (3:3:0) (m) Prerequisite: Math. 214.

Topics from partial differentiation, multiple integration, infinite series,

uniform convergence. Primarily for engineers and science majors.

321. Applied Ordinary Differential Equations. (3:3:0) Home Study also. Pre-

requisite: Math. 214.

Ordinary differential equations with applications; Fourier series; Laplace

transforms. Primarily for engineers and science majors.

322. Topics in Applied Mathematics. (3:3:0) Home Study also. Prerequisite:

Math. 214.

Linear algebra, vector calculus, and Fourier analysis. For engineers and

science majors.

323. Applied Partial Differential Equations. (3:3:0) Home Study also. Prerequi-

site: Math. 321.

Boundary value problems; transform methods; Fourier series; Bessel

functions; Legendre polynomials. Primarily for engineers and science

majors.

332. Introduction to Complex Analysis. (3:3:0) Prerequisite: Math. 214 or 244.

Complex algebra; analytic functions; integration in the complex plane;

infinite series; theory of residues; conformal mapping.

371, 372. Abstract Algebra. (3:3:0 ea.) Prerequisite: Math. 142, 214, or 111

and 301.

Preliminary examination of algebraic systems: groups, rings, fields, vector

spaces, linear transformations, matrices, etc.

385. Linear Algebra. (3:3:0) Prerequisite: Math. Ill or 301.

Vectors and matrices; linear equations; determinants; characteristic

values; linear operators; quadratic forms; etc.

MATHEMATICS 391

387. Theory of Numbers. (3:3:0) Prerequisite: Math. Ill or 301.

Foundations of number theory; congruences; residues; reciprocity law;

Diophantine equations.

411. Numerical Methods. (3:3:0) Prerequisites: Comput. Sci. 130; Math. 214

or 244. Recommended: Math. 322 or 372 or 385.

Interpolation; approximation; differentiation; integration; ordinary differ-

ential equations; and systems of equations, both linear and nonlinear.

434. Introduction to Ordinary Differential Equations. (3:3:0) Home Study also.

Prerequisite: Math. 214 or 244.

Methods and theory of ordinary differential equations.

436. Introduction to Partial Differential Equations. (3:3:0) Prerequisite: Math.

321 or 434.

Methods for solving the wave, heat, and Laplace equations; eigenvalue

problems and Fourier series.

451. Modern Geometry I. (3:3:0) Prerequisite: Math. 301 or 371.

Synthetic and analytic projective geometry; affine and Euclidean geom-

etry. Geometry by invariants of groups of transformations.

452. Modern Geometry II. (3:3:0) Prerequisite: Math. 451.

Relationships of geometry to algebra, supplemental design, and combina-

torial mathematics.

495R. Readings in Mathematics. (1-2:0:1-3 ea.) Prerequisite: consent of in-

structor.

Directed readings beyond the scope of usual undergraduate courses. Of-

fered on demand.

501. Real Numbers. (3:3:0) Prerequisite: Math. 371. Recommended: Math. 451.

Extensive examination of various Eixiomatic descriptions of the real num-

bers and the interrelationships among these descriptions. Offered on de-

mand.

502. Set Theory. (3:3:0) Prerequisite: Math. 371.

Zermelo-Fraenkel axioms for set theory; the axiom of choice; ordinal and

cardinal numbers; algebra of sets. Offered on demand.

508. Mathematical Logic. (3:3:0) Prerequisite: Math. 371 or 541.

Prepositional and first-order predicate calculi; set theories; well-ordering;

transfinite induction.

512. Introduction to Numerical Analysis. (3:3:0) Prerequisite: Math. 411.

Theory of constructive methods in mathematical analysis.

513R. Advanced Topics in Applied Mathematics. (3:3:0 ea.) Prerequisite: con-

sent of instructor.

Offered on demand.

541, 542. Introduction to Real Analysis. (3:3:0 ea.) Prerequisite: Math. 244

or 315.

A rigorous treatment of continuity, differentiability, integration of func-

tions of real variables, and infinite series.

551, 552. Introduction to Topology. (3:3:0 ea.) Prerequisite: completion of or

concurrent registration in Math. 541.

Axiomatic treatment of linearly ordered spaces, metric spaces, arcs, and

Jordan curves; types of connectedness.

585. Matrix Analysis. (3:3:0) Prerequisite: Math. 322, 372, or 385.

Characteristic values, canonical forms, and functions of matrices, with ap-

plications.

629. Teaching Mathematics in Secondary Schools. (3:3:0)

Offered on demand.

392 MATHEMATICS

631, 632. Complex Analysis. (3:3:0 ea.) Prerequisites: Math. 332, 542.

Offered 1972-73 and alternate years.

634, 635. Theory of Ordinary Differential Equations. (3:3:0 ea.) Prerequisites:

Math. 434, 512.

Offered 1973-74 and alternate years.

641, 642. Functions of a Real Variable. (3:3:0 ea.) Prerequisite: Math. 542.

Offered 1973-74 and alternate years.

643R. Special Topics in Analysis. (3:3:0 ea.) Prerequisites: Math. 541, 542.

Topics selected from continued fractions, stochastic processes, generalized

functions, etc.

645. Tensor Analysis. (3:3:0) Prerequisite: Math. 244 or 542.

Offered on demand.

647, 648. Theory of Partial Differential Equations. (3:3:0 ea.) Prerequisites:

Math. 436, 542.

Offered 1972-73 and alternate years.

651, 652. General Topology I, II. (3:3:0 ea.) Prerequisite: consent of instructor.

653R. Special Topics in Geometry. (3:3:0 ea.) Prerequisites: Math. 372, 452.

Topics from n-dimensional projective and algebraic geometry, founda-

tions, transformations, curves and surfaces, and sheaf theory.

655R. Advanced Special Topics in Topology. (3:3:0 ea.) Prerequisite: consent of

instructor.

Offered on demand.

661, 662. Functional Analysis. (3:3:0 ea.) Prerequisite: Math. 632 or 642.

Offered on demand.

671, 672. Modern Algebra. (3:3:0 ea.) Prerequisites: Math. 371, 372.

Offered 1973-74 and alternate years.

675R. Special Topics in Algebra. (3:3:0 ea.) Prerequisite: Math. 671.

Group theory; commutative algebra; homological algebra; ring theory;

algebraic number theory.

681. Linear Algebra. (3:3:0) Prerequisites: Math. 371, 372.

Offered 1972-73 and alternate years.

695. Readings in Mathematics. (1-2:1-2:0)

Offered on demand.

699. Thesis for Master's Degree. (6-9:Arr.:Arr.)

MECHANICAL ENGINEERING SCIENCE 393

MechonicQ

Engineering

Professors: Anderson, Cannon, Free, Heaton, Polve, Simonsen (Chairman, 223B

FELB), Ulrich, Warner, Wille.

Associate Professor: Paxson.

Assistant Professor: Chase.

The Mechanical Engineering Science Department offers a professional engineering

program at the bachelor, master, and doctoral levels. The curriculum is fully

accredited by the Engineers' Council for Professional Development (ECPD).

Mechanical engineering is a creative branch of applied science that deals with

the analysis, design, development, fabrication, and application of products that

are of a predominately mechanical nature. Various subdivisions of mechanical

engineering are described below in the section entitled "Specialized Options."

The training program at BYU which leads to a degree in mechanical engineer-

ing is built upon a sound basis of mathematics, physics, and chemistry. The

engineering classroom and laboratory course work is taught by a faculty with

extensive academic and industrial experience. The technical program is supple-

mented by a well-balanced program of social sciences, religion, biological sciences,

and humanities. The professional nature of this training program enables the

graduate to be immediately productive upon graduation as well as to keep up

with new technological developments.

Mechanical engineering by its very nature includes many varieties of special-

ization. All students are provided with a central core of engineering fundamentals.

By proper selection of elective courses, a student can increase his depth in such

specialized areas as (1) aerospace, (2) automatic controls and systems analysis,

(3) bioengineering, (4) manufacturing and industrial engineering, (5) materials

and metallurgy, (6) mechanical design, (7) nuclear engineering, (8) solid

mechsinics, (9) thermoscience, and (10) vibration and dynamics. Each student

is assigned an adviser, who works with him in developing his individual program.

Students who are inclined toward more routine technical work should consult

the offerings of the College of Industrial and Technical Education.

Recommend High School Preparation

Special recommendations for incoming engineering students are contained in the

College of Physical and Engineering Sciences section of this catalog. A qualified

student who has sufficient high school preparation can complete the Bachelor of

Science degree program in four academic years. This time can be reduced by

attending school during the Spring and Summer terms. However, the degrees

offered by the department are awarded for competence level attained rather

than for a fixed number of years' attendance. Therefore, students with insuffi-

cient high school preparation may require additional classes to complete the

degree requirements, whereas those with more than adequate preparation can re-

duce the number of classes normally required.

Civil Engineering 101 (Introduction to Engineering Graphics) and Math. Ill

(College Algebra and Trigonometry) are prerequisites to the engineering program.

Students who pass placement tests given prior to registration will be excused

394 MECHANICAL ENGINEERING SOENCE

O M

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MECHANICAL ENGINEERING SCIENCE 395

from taking these classes. Students who have sufficient preparation can also re-

ceive credit for History 170 and Health 130 — both required classes — by taking

special examinations.

Grade Requirements

To receive a bachelor's degree in mechanical engineering science, a student must

complete courses satisfying University general education requirements and

departmental requirements with a cumulative grade-point average of at least

2.00 (C). A maximum of 9 hours of D credit may be applied toward fulfilling

departmental requirements.

The graduate school requirement of a minimum 3.00 grade-point average

applies to all graduate degree programs. A minimum GPA of 2.50 is required in

the last 60 hours of course work prior to taking courses for graduate credit.

Students pursuing the integrated bachelor's-master's program for the Master of

Engineering degree should take special note of this, since they usually need to

apply for graduation admission during the junior year.

Suggested Course Sequences

Course sequences are outlined below for both the combined Bachelor of Science-

Master of Engineering program and for the Bachelor of Science only program.

The combined program is the generally recommended path leading to a pro-

fessional career in engineering practice. The B.S. program is designed for careers

in such fields as law, medicine, sales work, or other employment requiring less

engineering training.

Sequences for the combined five-year program and for the four-year program

are outlined by year and are also shown in flow charts with lines indicating

prerequisites. The prerequisite lines indicate how courses build upon each other.

In addition, a three-year B.S. program is outlined by year to show how the total

time may be shortened by attending school during the Spring and Summer

terms. The combined B.S. and M.E. program can, in a similar fashion, be com-

pleted in four years.

Combined B.S. and M.E. Degree Five- Year Program

First Year F

Mech. Eng. 101, 151 2

Civ. Eng. 102

Math. 112, 113 4

Physics 121, 122 3

Engl. Ill 3

♦Health 130 2

*Hist. 170

Relig. 121, 122 2

P.E. i

Dev. Assy. i

W

2

2

4

3

Total hours

17

17

Second Year

F

W

Mech. Eng. 201, 351

2

3

Civ. Eng. 201

2

Chem. 105, 106

4

4

Math. 214, 321

3

3

Physics 221

3

Physics 214

1

Stat. 332

2

Religion

2

2

P.E.

1

1

Dev. Assy.

i

i

Third Year

Mech. Eng. 321, 322

Mech. Eng. 363

Civ. Eng. 303, 304

Elec. Eng. 301

Math. 322

Engl. 316

Gen. ed. electives

Religion

Dev. Assy.

Total hours

Fourth Year

Mech. Eng. 412, 510

Mech. Eng. 534, 540

Mech. Eng. 431, 454

Elec. Eng. 302, 304

Elec. Eng. 303, 305

Math. 323

Gen. ed. electives

Dev. Assy.

Total hours

F

31

3i

3

2

1

W

4

3

2

3

2

2

17J 16i

W

31

31

3

2

1

3

165 16i

Total hours

16 17

396 MECHANICAL ENGINEERING SCIENCE

Fifth Year

F

W

Civ. Eng. 471

3

Mech. Eng. 471, 698

3

3

Gen. ed. electives

4

2

Mech. Eng. 591

h

—

Tech. electives

9

8

Total hours

16J

16

B.S. Degree Four-Year Program

First and second years are the same as combined B.S. and M. Eng. 5-year pro-

gram.

Third Year F W

Mech. Eng. 321, 322 3 4

Mech. Eng. 363 2

Civ. Eng. 303, 304 3 3

Elec. Eng. 301 2

Engl. 316 3

Gen. ed. electives 4 6

Religion 2 2

Dev. Assy. i i

Total hours 17* 171 Total hours 16i 171

Fourth Year

F

W

Mech. Eng. 412, 471

3i

3

Mech. Eng. 431, 454

3

3

Tech. electives

3h

6

Civ. Eng. 471

3

Elec. Eng. 302 or 304

2

Elec. Eng. 303 or 305

1

Gen. ed. electives

3

2

Dev. Assy.

h

i

B.S. Degree Three- Year Program

First Year F W Sp

Mech. Eng. 101, 151 2 2

Civ. Eng. 102, 201 2 2

Math. 112, 113, 214 4 4 3

Physics 121, 122 3 3

Engl. Ill 3

*Health 130 2

*Hist. 170 3

Gen. ed. elective 3

Relig. 121, 122 2 2

P.E. i h

Dev. Assy. I i

Total hours 17 17 8

Second Year F W Sp

Mech. Eng. 201 2

Mech. Eng. 321, 363 3 2

Civ. Eng. 303, 304 3 3

Chem. 105, 106 4 4

Math. 321 3

Stat. 332 2

Physics 221 3

Physics 214 1 Total hours

Engl. 316 3

*History 170 and Health 130 can be passed by examination.

Gen. ed. electives

Religion

P.E.

Dev. Assy.

Total hours

Third Year F

Mech. Eng. 412 3i

Mech. Eng. 322 4

Mech. Eng. 431,

454, 471 3

Mech. Eng. 351 3

Tech. electives

Civ. Eng. 471

Elec. Eng. 301. 302

or 304

Elec. Eng. 303

or 305

Gen. ed. electives 4