Randolph Goldman PH.D.

College of Natural and Computational Sciences - Department of Mathematics

ASSOCIATE PROFESSOR OF MATHEMATICS
CHAIR, DEPARTMENT OF MATHEMATICS

Education:

• Ph.D., Logic and Methodology of Science, University of California at Berkeley
• M.A., Mathematics, University of California at Berkeley
• M.S., Computer Science, University of California at Santa Cruz,
• J.D., University of Hawaii at Manoa
• B.A., Mathematics, University of California at Berkeley

Courses Taught:

• MATH 1150 Pre-Calculus I and II Accelerated
• MATH 2214 Calculus I
• MATH 2215 Calculus II
• MATH 3000 Proof Writing
• MATH 3110 Foundations of Math Logic and Application
• MATH 3234 Mathematical Cryptography
• MATH 3305 Linear Algebra
• MATH 3307 Differential Equations
• MATH 3320 Set Theory
• MATH 3301 Discrete Mathematics
• MATH 3460 Probability
• MATH 4210 Topology
• MATH 4301 Combinatorics and Graph Theory
• MATH 4330 Abstract Algebra
• MATH 4450 Real Analysis

Research Interests:

Mathematical Logic including Modal Logic; and Metamathematics.

For my publication on the semantics of third order modal logic, see

Gödel’s Property Abstraction Operator and Possibilism, Australasian Journal of Logic, managing editor Ed Mares, University of Wellington at Victoria, ISSN (electronic): 1448-5052 (11-2) 2014 Article no. 3

"For my paper discussing Charles Chihara's philosophy of Mathematics including Joel Hamkins' multiverse view in Set theory and Forcing" see

The Evolution of Chihara's Anti-Nominalistic Nominalism Regarding the Existence of Mathematical Objects, Australasian Journal of Logic, managing editor Ed Mares, University of Wellington at Victoria, (21:4) 2024, Article no. 2

Professional Interests:

Recursion Theory; Model Theory including Saturated Model Theory; Set Theory including Metamathematics of Set Theory; Real Analysis and Topology; Measure Theory and Lebesque Integration; Non-standard Analysis; Abstract Algebra; Complex Analysis; Functional Analysis; Discrete Mathematics; Combinatorial Mathematics; Computational and Descriptive Complexity; Algorithms

Personal Interests/Biography:

I am very interested in mentoring talented and ambitious students in mathematical logic. At Hawaii Pacific University I have been able to have success teaching advanced theorems more typically taught in graduate school such as the Gödel’s First and Second Incompleteness Theorems and Tarski’s Theorem to interested undergraduate students. In my advanced logic class, students learn how to use the Compactness Theorem of First Order Logic to obtain a non-model of the reals that includes infinitesimals and perform non-standard analysis. Some of my students have been accepted to graduate programs at elite universities such as University of California at Berkeley and MIT. One of my students learned an entire year of advanced Model Theory culminating in a lecture on Direct Systems of Structures and Elimination of Quantifiers. In his second year, he studied the Independence of the Continuum Hypothesis with an introduction to Forcing. Another one of my students learned Advanced Recursion Theory including Turing Degrees.

I believe that mathematical logic can be very empowering to students and that the introduction of elegant proofs in logic to undergraduate students can be inspirational and transformational. To read more about the opportunities to study mathematical logic at Hawaii Pacific University, please see the listings for MATH 3110, 3320, and 4301 in our Course Catalog