MSAE E

Prerequisites: CHEM UN1404 and PHYS UN1011

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (MSAE E3010) MSAE E3010 Lectures and hands-on experiments on the characterization of microstructure in crystalline and amorphous solids. Optical, scanning and transmission electron microscopy. Metallography, sample preparation and analysis. Stereology. Crystal structure determination with x-ray diffraction. Elemental analysis using energy-dispersive x-ray analysis. Atomic force microscopy

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (MSAE E3011) MSAE E3012 Metallographic sample preparation, optical microscopy, quantitative metallography, hardness and tensile testing, plastic deformation, annealing, phase diagrams, brittle fracture of glass, temperature and strain-rate dependent deformation of polymers; written and oral reports. This is the second of a two-semester sequence materials laboratory course

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: CHEM UN1403 or PHYS UN1403 or APMA E2101 Or equivalent

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

An introduction to the basic thermodynamics of systems, including concepts of equilibrium, entropy, thermodynamic functions, and phase changes. Basic kinetic theory and statistical mechanics, including diffusion processes, concept of phase space, classical and quantum statistics, and applications thereof

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: Senior standing. Written permission from instructor and approval from adviser. E3156: a design problem in materials science or metallurgical engineering selected jointly by the student and a professor in the department. The project requires research by the student, directed reading, and regular conferences with the professor in charge. E3157: completion of the research, directed reading, and conferences, culminating in a written report and an oral presentation to the department

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: Senior standing. Written permission from instructor and approval from adviser. E3156: a design problem in materials science or metallurgical engineering selected jointly by the student and a professor in the department. The project requires research by the student, directed reading, and regular conferences with the professor in charge. E3157: completion of the research, directed reading, and conferences, culminating in a written report and an oral presentation to the department

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: MSAE E3010 Or equivalent or permission of the instructor

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: Written permission from instructor and approval from adviser. May be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.S. degree requirements. Candidates for the B.S. degree may conduct an investigation in materials science or carry out a special project under the supervision of the staff. Credit for the course is contingent upon the submission of an acceptable thesis or final report

Subject

MSAE E

Credits (min)

0

Credits (max)

4

Credit unit

points

Type

course

Repeatable

May be repeated for credit, but no more than 6 points of this course may be counted toward the satisfaction of the B.

Edition

2026

Source

bulletin.columbia.edu

Subject

MSAE E

Credits (min)

2

Credits (max)

2

Type

course

Edition

2025-2026

Source

bulletin.columbia.edu

Prerequisites: (APPH E3100) and (MSAE E3010) or their equivalents with instructor's permission.

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (CHEM UN1403) and (PHYS UN1403) and (APMA E2101) or APMA E2101 AND CHEM W1403 AND PHYS W1403; or equivalent. A first course on crystallography. Crystal symmetry, Bravais lattices, point groups, space groups. Diffraction and diffracted intensities. Exposition of typical crystal structures in engineering materials, including metals, ceramics, and semiconductors. Crystalline anisotropy

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (MSAE E3010) or equivalent or instructors permission

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (CHEM UN1404) or or equivalent undergraduate thermodynamics.

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (MSAE E4100) or MSAE E4100; or instructor's permission. Phenomenological theoretical understanding of vibrational behavior of crystalline materials; introducing all key concepts at classical level before quantizing the Hamiltonian. Basic notions of Group Theory introduced and exploited: irreducible representations, Great Orthogonality Theorem, character tables, degeneration, product groups, selection rules, etc. Both translational and point symmetry employed to block diagonalize the Hamiltonian and compute observables related to vibrations/phonons. Topics include band structures, density of states, band gap formation, nonlinear (anharmonic) phenomena, elasticity, thermal conductivity, heat capacity, optical properties, ferroelectricty. Illustrated using both minimal model Hamiltonians in addition to accurate Hamiltonians for real materials (e.g., Graphene)

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (MSAE E3010) or equivalent or instructor's permission.

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (MSAE E4201) MSAE E4201 Review of thermodynamics, irreversible thermodynamics, diffusion in crystals and noncrystalline materials, phase transformations via nucleation and growth, overall transformation analysis and time-temperature-transformation (TTT) diagrams, precipitation, grain growth, solidification, spinodal and order-disorder transformations, martensitic transformation

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: MSAE E4200 Or instructor's permission

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: PHYS W1401 AND PHYS C1402 AND PHYS W1403; or equivalent. A survey course on the electronic and magnetic properties of materials, oriented towards materials for solid state devices. Dielectric and magnetic properties, ferroelectrics and ferromagnets. Conductivity and superconductivity. Electronic band theory of solids: classification of metals, insulators, and semiconductors. Materials in devices: examples from semiconductor lasers, cellular telephones, integrated circuits, and magnetic storage devices. Topics from physics are introduced as necessary

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Subject

MSAE E

Type

course

Edition

2026-2027

Source

bulletin.columbia.edu

Prerequisites: (APPH E3100 and MSAE E3111) or (CHEM BC3253 and CHEM GU4230) or (PHYS GU4021 and PHYS GU4023) or (MSAE E4200) or (MSAE E4203) or (MSAE E4206) Experience with a Unix interface (Linux/macOS), and Python programming are a plus. Or instructor’s permission.

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (MSAE E3010) Recommended preparation: a course in mechanics of materials.

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (MSAE E3010) and (MSAE E3013) Or instructor's permission. Corequisites: MSAE E3013,MSAE E3010

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (CHEM UN1403) and (MSAE E3010) or CHEM W1403 AND MSAE E3010; or equivalents or instructor's permission.

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: Introductory materials course or equivalent or instructor's permission. General experimental techniques in materials science, including X-ray diffraction, scanning electron microscopies, atomic force microscopy, materials synthesis and thermodynamics, characterization of material properties (mechanical, electrochemical, magnetic, electronic). Additional experiments at discretion of instructor

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: Instructor's permission. May be repeated for credit. Topics and instructors change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, and other fields

Subject

MSAE E

Credits (min)

1

Credits (max)

3

Credit unit

points

Type

course

Repeatable

May be repeated for credit.

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: Internship and approval from adviser must be obtained in advance. Only for master's students in the Department of Applied Physics and Applied Mathematics who may need relevant work experience as part of their program of study. Final report required. May not be taken for pass/fail or audited

Subject

MSAE E

Credits (min)

1

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: (APPH E3100) or APPH E3100; or equivalent. Basics of density functional theory (DFT) and its application to complex materials. Computation of electronics and mechanical properties of materials. Group theory, numerical methods, basis sets, computing, and running open source DFT codes. Problem sets and a small project

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: Instructor's permission.

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Or an E&M course, such as APPH E4300 APPLIED ELECTRODYNAMICS or PHYS GR6092 ELECTROMAGNETIC THEORY.

Subject

MSAE E

Credits (min)

1

Credits (max)

1

Type

course

Edition

2026-2027

Source

bulletin.columbia.edu

Vacuum basics, deposition methods, nucleation and growth, epitaxy, critical thickness, defects properties, effect of deposition procedure, mechanical properties, adhesion, interconnects, and electromigration

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: Written permission from instructor and approval from adviser. Formal written reports and conferences with the appropriate member of the faculty on a subject of special interest to the student but not covered in the other course offerings

Subject

MSAE E

Credits (min)

0

Credits (max)

6

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

May be repeated for credit. Selected topics in materials science. Topics and instructors change from year to year. For students in engineering, physical sciences, biological sciences, and related fields

Subject

MSAE E

Credits (min)

3

Credits (max)

3

Credit unit

points

Type

course

Repeatable

May be repeated for credit.

Edition

2026

Source

bulletin.columbia.edu

Speakers from universities, national laboratories, and industry are invited to speak on the recent impact of materials science and engineering innovations

Subject

MSAE E

Credits (min)

0

Credits (max)

0

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu

Prerequisites: Qualifying examination for the doctorate. Required of doctoral candidates

Subject

MSAE E

Credits (min)

0

Credits (max)

15

Credit unit

points

Type

course

Edition

2026

Source

bulletin.columbia.edu