University of Texas at El Paso Academic Catalog

Academic Catalog

BS in Aerospace Engineering

The Aerospace Engineering curriculum is designed for students who desire to enter the aerospace or related industry or to pursue advanced studies in these areas. The curriculum provides a broad range of courses in the areas of aerodynamics, aerospace structures and aerospace and aeronautic vehicle design.

Vision

The Aerospace Engineering Program strives to graduate aerospace engineers of the highest quality and to conduct state-of-the-art research.

Marketable Skills

Students will gain the following marketable skills: 

  1. Confidence: Be self-assured through appreciating your own talents, abilities, skills, and qualities.
  2. Critical thinking: Analyze and evaluate issues in order to solve problems and develop informed opinions.
  3. Entrepreneurship: Develop, organize, and manage ideas and opportunities turning them into new products, services, firms, or industries.
  4. Leadership: Step up, think, and act critically and creatively to bring others together to accomplish a common task.
  5. Problem-solving: Find solutions to difficult or complex issues.
  6. Teamwork: Participate as an effective, efficient member of a group in order to meet a common goal.

Mission

The Aerospace Engineering program at The University of Texas at El Paso seeks to prepare students for careers in aerospace engineering and related disciplines. Successful achievement of this objective will be met if:

  • The majority of our graduates obtain meaningful employment in the aerospace or related industry after graduation
  • After five years most graduates are working in engineering
  • After five years most graduates have achieved their initial career goals and advanced their careers, i.e. promotion, pursuit of advanced degree, etc.
  • All graduates feel well served by the education they received at UTEP.

The program will consist of a largely common initial two years with the current B.S. in Mechanical Engineering degree program at UTEP but have course, laboratory and project experiences in the last two years of the curriculum that prepare students in: 

  • Aerodynamics,
  • Propulsion,
  • Aerostructures,
  • Aerospace dynamics and controls, and
  • Aerospace systems engineering

Admission Requirements

There are no additional admission requirements to the program above those of admission to the University of Texas at El Paso and to eligible to take MATH 1411 Calculus I or equivalent.

Degree Requirements

The degree requires 128 SCH which includes:

  1. completion of the university core curriculum (42 SCH)
  2. 56 SCH of prescribed courses,
  3. 30 SCH of engineering electives

Degree Plan

Designated Core
CE 2326Econ for Engrs & Scientists3
CHEM 1305
CHEM 1105
General Chemistry
and Laboratory for CHEM 1305
4
MATH 1508Precalculus3-5
or MATH 1310 Trigonometry and Conics
or MATH 1411 Calculus I
PHYS 2320
PHYS 2120
Introductory Mechanics
and Laboratory for PHYS 2320
4
University Core Curriculum(All courses require a grade of C or better.)
Complete the University Core Curriculum requirements.42
Aerospace Engineering (Other Requirements) (All courses require a grade of C or better.)
Required Courses: Some of these are included in the core.
CE 2326Econ for Engrs & Scientists3
MATH 1411Calculus I4
MATH 1312Calculus II3
MATH 2313Calculus III3
MATH 2326Differential Equations3
Math/Science Elective
Select one of the following: (Math courses in this section cannot be used to satisfy other degree requirements)3
Applied Analysis I
Linear Algebra
Numerical Analysis
Applied Analysis II
Survey of Modern Physics
Analytical Mechanics I
Probability and Statistics
Science Elective
Select one of the following:4
General Chemistry
and Laboratory for CHEM 1306
Introductory Electromagnetism
and Laboratory for PHYS 2321
Math Elective
Select one of the following:(Math courses in this section cannot be used to satisfy other degree requirements)
MATH 3335Applied Analysis I3
MATH 4329Numerical Analysis3
MATH 4336Applied Analysis II3
STAT 3320Probability and Statistics3
Aerospace Engineering Major
Required Courses:
MECH 1305Graphic & Design Fundamentals c3
MECH 1321Mechanics I-Statics c3
MECH 2103Engineering Computations c1
AERO 2311Intro to Thermal-fluid Sci3
MECH 2322Mechanics of Materials c3
MECH 2340Mechanics II -Dynamics c3
MECH 2342Electro Mechanical Systems c3
AERO 2331
AERO 2131
Aerospace Materials
and Aerospace Materials Lab
4
AERO 3113Thermo-fluid Lab1
AERO 3312Aerodynamics 13
AERO 3323Aerospace Structures I3
AERO 3343Systems Modelling and Control3
AERO 3365Aerospace Systems Engineering3
Laboratory Experience
Select one of the following:1
Mechatronics Lab
Aero-Pre-professional Exp.
Aeronautical Engineering Concentration 1
AERO 4311Flight Dynamics and Controls3
AERO 4312Aircraft Design3
AERO 4322Aerospace Propulsion3
AERO 4366Aerospace Senior Design3
Aeronautical Eng Concentration Electives
Must take 3 courses9
Aerospace Structures II
Special Topics in Aeronautics
Special Topics Aerostructures
Aerodynamics II
Hypersonic Vehicle Design
Structural Dynamics
Special Topics in Hypersonics
Approved TECH Electives
Must take 2 courses6
Aerospace Structures II
Spacecraft Att. Dyn. & Cntrls
Orbital Mechanics
Space Environments
Space Mission & Vehicle Design
Rocket Propulsion
Special Topics in Astronautics
Aerospace Communications
Astronautical Engineering Concentration 1
AERO 4351Orbital Mechanics3
AERO 4355Space Mission & Vehicle Design3
AERO 4357Rocket Propulsion3
AERO 4368ASTRO Senior Design3
Astronautical Eng Concentration Electives
Must take 3 courses9
Aerospace Structures II
Spacecraft Att. Dyn. & Cntrls
Space Environments
Special Topics in Astronautics
Aerospace Communications
Approved TECH Electives
Must take 2 courses6
Flight Dynamics and Controls
Aircraft Design
Aerospace Structures II
Special Topics in Aeronautics
Aerospace Propulsion
Special Topics Aerostructures
Aerodynamics II
Hypersonic Vehicle Design
Structural Dynamics
Special Topics in Hypersonics
Total Hours128

C Course requires a grade of C or better
1 Must declare a concentration and take three classes from the declared concentration area
3 Must be in the last full semester and have a 2.0 GPA or better in major.

University Core Curriculum (A program may recommend specific courses. All courses require a C or better.)

I. Communication (six hours)

Courses in this category focus on developing ideas and expressing them clearly, considering the effect of the message, fostering understanding, and building the skills needed to communicate persuasively. Courses involve the command of oral, aural, written, and visual literacy skills that enable people to exchange messages appropriate to the subject, occasion, and audience. Course objectives for this component are: Critical Thinking Skills, Communication Skills, Teamwork, and Personal Responsibility.
Select six hours of the following:6
For students whose secondary education was in English:
Writing About Literature
Rhetoric & Composition I
Rhetoric & Composition 2
For students whose secondary education was not in English:
Expos Engl Compos-Spkr Esl
Res & Crit Writng Spkr Esl
TOTAL HOURS6

II. American History (six hours)

Courses in this category focus on the consideration of past events and ideas relative to the United States, with the option of including Texas History for a portion of this component area. Courses involve the interaction among individuals, communities, states, the nation, and the world, considering how these interactions have contributed to the development of the United States and its global role. Course objectives for this component are: Critical Thinking Skills, Communication Skills, Social Responsibility, and Personal Responsibility.
HIST 1301History of U.S. to 18653
HIST 1302History of U.S. Since 18653
TOTAL HOURS6

III. Language, Philosophy & Culture (three hours)

Courses in this category focus on how ideas, values, beliefs, and other aspects of culture express and affect human experience. Courses involve the exploration of ideas that foster aesthetic and intellectual creation in order to understand the human condition across cultures. Course objectives for this component are: Critical Thinking Skills, Communication Skills, Social Responsibility, and Personal Responsibility.
Select one of the following:3
Language in Culture & Society
Intro-African Amer Studies
Latina/o Presence in the U.S.
English Literature
English Literature
Intro to American Poetry
Language in Culture & Society
Making of the "Other" Americas
World History to 1500
World History Since 1500
Language in Culture & Society
Introduction to Philosophy
Ethics
Introduct to Religious Studies
Seeing & Naming: Conversations
Introduction to Womens Studies
Global Feminisms
TOTAL HOURS3

IV. Mathematics (three hours)

Courses in this category focus on quantitative literacy in logic, patterns, and relationships. Courses involve the understanding of key mathematical concepts and the application of appropriate quantitative tools to everyday experience. Course objectives for this component are: Critical Thinking Skills, Communication Skills, and Empirical & Quantitative Skills.
Select one of the following:3
College Algebra
Trigonometry and Conics
Math in the Modern World
Math for Social Sciences I
Calculus I
Precalculus
Math for Social Sciences II
Statistical Literacy
Elementary Statistical Methods
TOTAL HOURS3

V. Life & Physical Sciences (six hours)

Courses in this category focus on describing, explaining, and predicting natural phenomena using the scientific method. Courses involve the understanding of interactions among natural phenomena and the implications of scientific principles on the physical world and on experiences. Course objectives for this component are: Critical Thinking Skills, Communication Skills, Empirical & Quantitative Skills, and Teamwork.
Required: Lecture/Lab Sequence plus Additional Lecture
Astronomy Lab I
Elem Astronomy-Solar System
Elem Astr Stars & Galaxies
Introductory Biology Lab
Human Biology Laboratory
Topics in Study of Life I
Organismal Biology Laboratory
Introductory Biology
Human Biology
General Biology
Organismal Biology
Human Anat/Physio Lab I
Human Anat/Physio Lab II
Human Anat/Physiology I
Human Anat/Physiology II
Laboratory for CHEM 1305
Laboratory for CHEM 1306
Intro General Chemistry Lab
Intro Organic & Biochem Lab
General Chemistry
General Chemistry
Intro to General Chemistry
Intro Organic & Biochemistry
Environmental Sci. Lab
Non-major Lab for ESCI 1301
Intro to Environmental Sci
Laboratory for GEOG 1306
Physical Geography
Lab for GEOL 1313
Lab for GEOL 1314
Principles of Earth Sci - Lab
Laboratory for Geology 1212
Principles of Earth Sciences
Principles of Earth Science
Natural Hazards
Intro to Physical Geology
Intro to Historical Geol
Fundamentals of Nutrition
Wellness Dynamics
Microorganisms and Disease
General Physics I
General Physics II
Laboratory for PHYS 2320
Laboratory for PHYS 2321
Introductory Mechanics
Introductory Electromagnetism
TOTAL HOURS6

VI. Political Science (six hours)

Courses in this category focus on consideration of the Constitution of the United States and the constitutions of the states, with special emphasis on that of Texas. Courses involve the analysis of governmental institutions, political behavior, civic engagement, and their political and philosophical foundations. Course objectives for this component are: Critical Thinking Skills, Communication Skills, Social Responsibility and Personal Responsibility.
Required Courses:
POLS 2310Introduction to Politics3
POLS 2311American Gover & Politics3
TOTAL HOURS6

VII. Social & Behavioral Sciences (three hours)

Courses in this category focus on the application of empirical and scientific methods that contribute to the understanding of what makes us human. Courses involve the exploration of behavior and interactions among individuals, groups, institutions, and events, examining their impact on the individual, society, and culture. Course objectives for this component are: Critical Thinking Skills, Communication Skills, Empirical & Quantitative Skills, and Social Responsibility.
Select one of the following:3
Origins of Humanity
World Cultures
Cultural Geography
Introduction to Human Language
Asian American Studies
Econ for Engrs & Scientists
Intro to Chicano Studies
Interpersonal Communication
Principles of Macroeconomics
Principles of Microeconomics
Introduction to Human Language
Cultural Geography
Leadership in Action
Introduction to Human Language
Introduction to Psychology
American Society
Cultural Geography
TOTAL HOURS3

VIII. Creative Arts

Courses in this category focus on the appreciation and analysis of creative artifacts and works of the human imagination. Courses involve the synthesis and interpretation of artistic expression and enable critical, creative, and innovative communication about works of art. Course objectives for this component are: Critical Thinking Skills, Communication Skills, Teamwork, and Social Responsibility.
Select one of the following:3
Art Appreciation
History of Art I
History of Art II
Chicana/o Fine Arts Appreciat
Writing in the Contemp World
Introduction to Dance
Intro-Art of Motion Pict.
Music Appreciation
Jazz to Rock
Music, Culture, and Society
Introduction to Theatre
TOTAL HOURS3

IX. Component Area Option (six hours)

a. A minimum of 3 SCH must meet the definition and corresponding Core Objectives specified in one of the foundational component areas. b. As an option for up to 3 semester credit hours of the Component Area Option, an institution may select course(s) that: (i) Meet(s) the definition specified for one or more of the foundational component areas; and (ii) Include(s) a minimum of three Core Objectives, including Critical Thinking Skills, Communication Skills, and one of the remaining Core Objectives of the institution's choice.
Science and Society
Human Variation
Intro to Indigenous Studies
Intro to Global Business
Public Speaking
Business/Profession Comm
Intro-Computational Thinking
Computer Programming Sci/Engr
Intro to Physical Computing
Eng Innovation and Leadership
Engineering Design Experience
Applied Engineering Analysis
Physcl Actvty for Hth & Well
Introduction to Leadership
Intro to Indigenous Studies
Inquiry in Math & Science
Science and Society
Intro to Indigenous Studies
Comm. Var. Across the Lifespan
Seminar/Critical Inquiry
TOTAL HOURS6

4-Year Sample Degree Plan

BS Aerospace Engineering, Aeronautical Engineering Concentration [Starting with Calculus]

FRESHMAN
Fall
MECH 1305Graphic & Design Fundamentals +3
RWS 1301Rhetoric & Composition I +3
MATH 1411Calculus I +4
PHYS 2320
PHYS 2120
Introductory Mechanics
and Laboratory for PHYS 2320
4
CS 1310Intro-Computational Thinking (Component Area) +3
or CS 1320 Computer Programming Sci/Engr
Spring
MECH 1321Mechanics I-Statics +3
HIST 1301History of U.S. to 1865 +3
RWS 1302Rhetoric & Composition 2 +3
MATH 1312Calculus II +3
CHEM 1305
CHEM 1105
General Chemistry
and Laboratory for CHEM 1305 +
4
SOPHOMORE
Fall
MECH 2322Mechanics of Materials +3
MATH 2313Calculus III +3
AERO 2311Intro to Thermal-fluid Sci +3
MECH 2103Engineering Computations +1
HIST 1302History of U.S. Since 1865 +3
PHYS 2321
PHYS 2121
Introductory Electromagnetism
and Laboratory for PHYS 2321 (Science Elective) +,1
4
Spring
MECH 2340Mechanics II -Dynamics +3
AERO 2131Aerospace Materials Lab1
AERO 2331Aerospace Materials +3
MECH 2342Electro Mechanical Systems +3
CE 2326Econ for Engrs & Scientists +3
MATH 2326Differential Equations3
JUNIOR
Fall
AERO 3113Thermo-fluid Lab1
AERO 3365Aerospace Systems Engineering3
AERO 3312Aerodynamics 13
AERO 3323Aerospace Structures I3
POLS 2310Introduction to Politics +3
Math Elective +,33
Spring
Lab Experience 21
COMM 1302Business/Profession Comm +3
AERO 3343Systems Modelling and Control3
Aeronautical Eng Concen. Electives I3
Science/Math Elective +,43
Creative Arts Course3
SENIOR
Fall
Language, Philosophy, and Culture Course +3
AERO 4312Aircraft Design3
AERO 4311Flight Dynamics and Controls3
AERO 4322Aerospace Propulsion3
AERO TECH Elective I3
Spring
AERO 4366Aerospace Senior Design3
Aeronautical Eng Concen. Electives II3
AERO TECH Elective3
Aeronautical Eng Concen. Electives III3
POLS 2311American Gover & Politics3
Total Hours128
+

Grade of C or better required

1

Must be either CHEM 1306 with CHEM 1106, PHYS 2321+2121 or by permission of advisor.

2

From the department approved list of Laboratory Experience courses.

3

Selected from MATH 3335, 4336, STAT 3320. By completing 3 of these electives you may be eligible for a Mathematics minor, interested students should consult the Department of Mathematics.

4

Approved courses are: PHYS 2325, PHYS 3351 PHYS 4348 or any course listed in NOTE 3 (not already taken).

5

Prerequisites depend on the concentration.

BS Aerospace Engineering, Aeronautical Engineering Concentration [Starting with Precalculus]

FRESHMAN
Summer
MATH 1508Precalculus5
Fall
MECH 1305Graphic & Design Fundamentals +3
RWS 1301Rhetoric & Composition I +3
MATH 1411Calculus I +4
PHYS 2320
PHYS 2120
Introductory Mechanics
and Laboratory for PHYS 2320
4
CS 1310Intro-Computational Thinking (Component Area) +3
or CS 1320 Computer Programming Sci/Engr
Spring
MECH 1321Mechanics I-Statics +3
HIST 1301History of U.S. to 1865 +3
RWS 1302Rhetoric & Composition 2 +3
MATH 1312Calculus II +3
CHEM 1305
CHEM 1105
General Chemistry
and Laboratory for CHEM 1305 +
4
SOPHOMORE
Fall
MECH 2322Mechanics of Materials +3
MATH 2313Calculus III +3
AERO 2311Intro to Thermal-fluid Sci +3
MECH 2103Engineering Computations +1
HIST 1302History of U.S. Since 1865 +3
PHYS 2321
PHYS 2121
Introductory Electromagnetism
and Laboratory for PHYS 2321 (Science Elective) +,1
4
Spring
MECH 2340Mechanics II -Dynamics +3
AERO 2131Aerospace Materials Lab1
AERO 2331Aerospace Materials +3
MECH 2342Electro Mechanical Systems +3
CE 2326Econ for Engrs & Scientists +3
MATH 2326Differential Equations3
JUNIOR
Fall
AERO 3113Thermo-fluid Lab1
AERO 3365Aerospace Systems Engineering3
AERO 3312Aerodynamics 13
AERO 3323Aerospace Structures I3
POLS 2310Introduction to Politics +3
Math Elective +,33
Spring
Lab Experience 21
COMM 1302Business/Profession Comm +3
AERO 3343Systems Modelling and Control3
Aeronautical Eng Concen. Electives I3
Science/Math Elective +,43
Creative Arts Course3
SENIOR
Fall
Language, Philosophy, and Culture Course +3
AERO 4312Aircraft Design3
AERO 4311Flight Dynamics and Controls3
AERO 4322Aerospace Propulsion3
AERO TECH Elective I3
Spring
AERO 4366Aerospace Senior Design3
Aeronautical Eng Concen. Electives II3
AERO TECH Elective3
Aeronautical Eng Concen. Electives III3
POLS 2311American Gover & Politics3
Total Hours133
+

Grade of C or better required

1

Must be either CHEM 1306 with CHEM 1106, PHYS 2321+2121 or by permission of advisor.

2

From the department approved list of Laboratory Experience courses.

3

Selected from MATH 3335, 4336, STAT 3320. By completing 3 of these electives you may be eligible for a Mathematics minor, interested students should consult the Department of Mathematics.

4

Approved courses are: PHYS 2325, PHYS 3351 PHYS 4348 or any course listed in NOTE 3 (not already taken).

5

Prerequisites depend on the concentration.

BS Aerospace Engineering, Astronautical Engineering Concentration [Starting with Calculus]

FRESHMAN
Fall
MECH 1305Graphic & Design Fundamentals +3
RWS 1301Rhetoric & Composition I +3
MATH 1411Calculus I +4
PHYS 2320
PHYS 2120
Introductory Mechanics
and Laboratory for PHYS 2320
4
CS 1310Intro-Computational Thinking (Component Area) +3
or CS 1320 Computer Programming Sci/Engr
Spring
MECH 1321Mechanics I-Statics +3
HIST 1301History of U.S. to 1865 +3
RWS 1302Rhetoric & Composition 2 +3
MATH 1312Calculus II +3
CHEM 1305
CHEM 1105
General Chemistry
and Laboratory for CHEM 1305 +
4
SOPHOMORE
Fall
MECH 2322Mechanics of Materials +3
MATH 2313Calculus III +3
AERO 2311Intro to Thermal-fluid Sci +3
MECH 2103Engineering Computations +1
HIST 1302History of U.S. Since 18653
PHYS 2321
PHYS 2121
Introductory Electromagnetism
and Laboratory for PHYS 2321 (Science Elective) +,1
4
Spring
MECH 2340Mechanics II -Dynamics +3
AERO 2131Aerospace Materials Lab1
AERO 2331Aerospace Materials +3
MECH 2342Electro Mechanical Systems +3
CE 2326Econ for Engrs & Scientists +3
MATH 2326Differential Equations3
JUNIOR
Fall
AERO 3113Thermo-fluid Lab1
AERO 3365Aerospace Systems Engineering3
AERO 3312Aerodynamics 13
AERO 3323Aerospace Structures I3
POLS 2310Introduction to Politics +3
Math Elective 33
Spring
Lab Experience 21
COMM 1302Business/Profession Comm +3
AERO 3343Systems Modelling and Control3
Astronautical Eng Concen. Electives I3
Science/Math Elective +,43
Creative Arts Course3
SENIOR
Fall
Language, Philosophy, and Culture Course +3
AERO 4351Orbital Mechanics3
AERO 4355Space Mission & Vehicle Design3
AERO 4357Rocket Propulsion3
ASTRO TECH Elective I3
Spring
AERO 4368ASTRO Senior Design3
Astronautical Eng Concen. Electives II3
ASTRO TECH Elective3
Astronautical Eng Concen. Electives III3
POLS 2311American Gover & Politics3
Total Hours128
+

Grade of C or better required

1

Must be either CHEM 1306 with CHEM 1106, PHYS 2321+2121 or by permission of advisor.

2

From the department approved list of Laboratory Experience courses.

3

Selected from MATH 3335, 4336, STAT 3320. By completing 3 of these electives you may be eligible for a Mathematics minor, interested students should consult the Department of Mathematics.

4

Approved courses are: PHYS 2325, PHYS 3351 PHYS 4348 or any course listed in NOTE 3 (not already taken).

BS Aerospace Engineering, Astronautical Engineering Concentration [Starting with Precalculus]

FRESHMAN
Summer
MATH 1508Precalculus5
Fall
MECH 1305Graphic & Design Fundamentals +3
RWS 1301Rhetoric & Composition I +3
MATH 1411Calculus I +4
PHYS 2320
PHYS 2120
Introductory Mechanics
and Laboratory for PHYS 2320
4
CS 1310Intro-Computational Thinking (Component Area) +3
or CS 1320 Computer Programming Sci/Engr
Spring
MECH 1321Mechanics I-Statics +3
HIST 1301History of U.S. to 1865 +3
RWS 1302Rhetoric & Composition 2 +3
MATH 1312Calculus II +3
CHEM 1305
CHEM 1105
General Chemistry
and Laboratory for CHEM 1305 +
4
SOPHOMORE
Fall
MECH 2322Mechanics of Materials +3
MATH 2313Calculus III +3
AERO 2311Intro to Thermal-fluid Sci +3
MECH 2103Engineering Computations +1
HIST 1302History of U.S. Since 18653
PHYS 2321
PHYS 2121
Introductory Electromagnetism
and Laboratory for PHYS 2321 (Science Elective) +,1
4
Spring
MECH 2340Mechanics II -Dynamics +3
AERO 2131Aerospace Materials Lab1
AERO 2331Aerospace Materials +3
MECH 2342Electro Mechanical Systems +3
CE 2326Econ for Engrs & Scientists +3
MATH 2326Differential Equations3
JUNIOR
Fall
AERO 3113Thermo-fluid Lab1
AERO 3365Aerospace Systems Engineering3
AERO 3312Aerodynamics 13
AERO 3323Aerospace Structures I3
POLS 2310Introduction to Politics +3
Math Elective 33
Spring
Lab Experience 21
COMM 1302Business/Profession Comm +3
AERO 3343Systems Modelling and Control3
Astronautical Eng Concen. Electives I3
Science/Math Elective +,43
Creative Arts Course3
SENIOR
Fall
Language, Philosophy, and Culture Course +3
AERO 4351Orbital Mechanics3
AERO 4355Space Mission & Vehicle Design3
AERO 4357Rocket Propulsion3
ASTRO TECH Elective I3
Spring
AERO 4368ASTRO Senior Design3
Astronautical Eng Concen. Electives II3
ASTRO TECH Elective3
Astronautical Eng Concen. Electives III3
POLS 2311American Gover & Politics3
Total Hours133
+

Grade of C or better required

1

Must be either CHEM 1306 with CHEM 1106, PHYS 2321+2121 or by permission of advisor.

2

From the department approved list of Laboratory Experience courses.

3

Selected from MATH 3335, 4336, STAT 3320. By completing 3 of these electives you may be eligible for a Mathematics minor, interested students should consult the Department of Mathematics.

4

Approved courses are: PHYS 2325, PHYS 3351 PHYS 4348 or any course listed in NOTE 3 (not already taken).