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Pages


Title

"For any letter we can substitute throughout the identity any expression containing a new letter...".

Abstract/Description

Writing rules for operations used in algebra problem and writing about their implications; Defining operators and notation for problem and writing about them; Possibly assigned work as the rules are numbered and the work is neat and wellwritten; Back of FSUDirac_12_3_1_0017.

Identifier

FSUDirac_12_3_1_0018

Format

Image (JPEG2000)


Title

"For any letter we can substitute throughout the identity any expression.".

Abstract/Description

Defining rules for certain expressions; Making notes about notation for these certain expressions; Giving examples using θ and ϕ.

Identifier

FSUDirac_12_3_5_0005

Format

Image (JPEG2000)


Title

"If an identity with n letters is to be true…".

Abstract/Description

Writing about mathematical identities and numbers in general; Back of FSUDirac_12_3_1_0018.

Identifier

FSUDirac_12_3_1_0017

Format

Image (JPEG2000)


Title

"mn + 1 = p is a prime…".

Abstract/Description

Apparent scratch work for number theoretical analysis; Possibly continuation of previous problem; Possibly multiple different problems worked on, including m, n, p problem, r, s, p problem, a, b, k problem, etc.

Identifier

FSUDirac_12_1c_0033

Format

Image (JPEG2000)


Title

"n is an odd prime, a, b, c are integers…".

Abstract/Description

Number theoretical analysis with apparent problem statement pertaining to n, a, b, and c; extensive algebra and calculation done with variables x, y, z.

Identifier

FSUDirac_12_1c_0032

Format

Image (JPEG2000)


Title

"s is a power of n".

Abstract/Description

Number theoretical analysis of primes, with apparent aim of solving a problem (number 1 in top right corner could be question number; problem is possibly to prove that s is a power of n, as is concluded in bottom right).

Identifier

FSUDirac_12_1c_0027

Format

Image (JPEG2000)


Title

"To obtain a particular case by putting two letters the same.".

Abstract/Description

Continuation of investigating algebraic rules from FSUDirac_12_3_1_0018; adding new rules to change system and analyzing the changes.

Identifier

FSUDirac_12_3_5_0001

Format

Image (JPEG2000)


Title

Academy of Sciences of Lisbon Award.

Creator

Academia das Ciencias de Lisboa

Abstract/Description

States that the title of "Correspondente" will be conferred upon Paul A. M. Dirac in recognition of his merits.

Date Issued

19530517

Identifier

2709718, s3b4f2

Format

Image (JPEG2000)


Title

Academy of Sciences of Turin Award.

Creator

Accademia delle scienze di Torino

Abstract/Description

Certificate awarding Paul A. M. Dirac with an honorary professorship at the University of Turin, Italy.

Date Issued

19511115

Identifier

s3b4f3, 2709710

Format

Image (JPEG2000)


Title

Algebraic manipulations, along with intersecting oval figures (with marked points of intersection).

Abstract/Description

Attempt to rewrite expression involving h, k, n2, n3 in order to substitute into equation with t1, t2, a, b to solve; many drawings of ovals, probably unrelated.

Identifier

FSUDirac_12_1b_0008

Format

Image (JPEG2000)


Title

Algebraic manipulations, doodled on an old stock offer.

Abstract/Description

Algebraic manipulations for a random problem.

Identifier

FSUDirac_12_1b_0005

Format

Image (JPEG2000)


Title

Algebraic manipulations, doodled on top of an old exercise paper.

Abstract/Description

Simple algebraic manipulations, doodled on a sheet used for a different problem (possibly an old exercise paper).

Identifier

FSUDirac_12_1b_0003

Format

Image (JPEG2000)


Title

American Academy of Arts and Sciences Award.

Creator

American Academy of Arts and Sciences

Abstract/Description

States that Dirac is a Foreign Honorary Member of the American Academy of Arts and Sciences, but has all of the rights and privileges of a member.

Date Issued

19500510

Identifier

s3b4f6, 2709708

Format

Image (JPEG2000)


Title

Analyses related to cubic and quintic polynomial equations.

Abstract/Description

Assigning values to expansions of quintic expressions in terms of a,b,c,d,e (similar to FSUDirac_12_1e_0001 and FSUDirac_12_1e_0006). Vieta’s formula. Writing quintic formula in terms of x,y,z,r, which are expressions in terms of ad. Rewriting general cubic equation.

Identifier

FSUDirac_12_1e_0008

Format

Set of related objects


Title

Analysis associated with reduced quintic polynomial equation.

Abstract/Description

Equating oneterm expressions in terms of ad and of power five to constants eh and attempt to construct equations of specific forms in terms in eh. Work with reduced quintic polynomial equation equal to zero.

Identifier

FSUDirac_12_1e_0022

Format

Set of related objects


Title

Analysis of a particular quintic polynomial equation.

Abstract/Description

Quintic equation the same as on FSUDirac_12_1d_0027; attempt to find products of expressions αδ that are possibly roots; assignment of constant to represent quotients of form ab/c in terms of ad (linked to FSUDirac_12_1e_0023).

Identifier

FSUDirac_12_1e_0009

Format

Set of related objects


Title

Analysis of factors using modular arithmetic.

Abstract/Description

Number theory analysis of factors using modular arithmetic; Possibly an assigned problem.

Identifier

FSUDirac_12_1c_0022

Format

Image (JPEG2000)


Title

Analysis of primes and factors using modular arithmetic.

Abstract/Description

Further number theoretical analysis of primes and factors of expressions using modular arithmetic.

Identifier

FSUDirac_12_1c_0024

Format

Image (JPEG2000)


Title

Analysis related to solving reduced cubic polynomial equation.

Abstract/Description

Writing sums of terms a through d raised to fractional powers; ω and i also used; solving reduced cubic equation.

Identifier

FSUDirac_12_3_1_0015

Format

Set of related objects


Title

Attempts to logarithmic and exponential equations.

Abstract/Description

Attempts to solve exponential and logarithmic equations; Possible attempts to match polynomial equations to logarithmic and exponential equations for alternate solution method.

Identifier

FSUDirac_12_1a_0019

Format

Image (JPEG2000)


Title

Axioms for rings.

Abstract/Description

Listing axioms for rings with two operations, addition, denoted by α, and multiplication, denoted by β.

Identifier

FSUDirac_12_3_5_0003

Format

Image (JPEG2000)


Title

Circuitry/electricity physics problem.

Abstract/Description

Working on circuitry/electricity physics problem (trying to calculate change in power); Possibly assigned for school.

Identifier

FSUDirac_12_3_5_0006

Format

Image (JPEG2000)


Title

Comparison of coefficients in different expansions.

Abstract/Description

Comparison of coefficients of terms in expansions of different summations/products of summations (like FSUDirac_12_1a_0011; FSUDirac_12_1d_0005); writing summations of products as quintic polynomials after substitution; comparison of coefficients of summated expressions up to degree 5 and assignment of values to each equation (e.g. 1, 5, 5. Possibly connected to Galois groups?)

Identifier

FSUDirac_12_1d_0011_polyeq, fsu:186636

Format

Set of related objects


Title

Construction of quintic expressions.

Abstract/Description

Construction of quintic expressions; Comparison of an expression raised to different degrees.

Identifier

FSUDirac_12_1a_0005

Format

Set of related objects


Title

Continued fractional term manipulations & permutations of x and y terms.

Abstract/Description

Continuation of FSUDirac_12_1a_0015 and FSUDirac_12_1a_0016 with composed fraction summation; Comparison between functions at certain points and summations; Matching of given x and y values and counting combinations between them.

Identifier

FSUDirac_12_1a_0017

Format

Image (JPEG2000)


Title

Determining HCFs.

Abstract/Description

Number theoretical analysis; Possibly a continuation of a set of related problems, with potential goal of finding H.C.F.s (number 4 in top right corresponds to numbers in top right of FSUDirac_12_1c_0027, FSUDirac_12_1c_0028 and FSUDirac_12_1c_0034).

Identifier

FSUDirac_12_1c_0029

Format

Image (JPEG2000)


Title

Diagrams for exercises.

Abstract/Description

Diagrams, of unknown origin or relationship.

Identifier

FSUDirac_12_1e_0006

Format

Image (JPEG2000)


Title

Expansions and factoring of terms in multiple variables.

Abstract/Description

Factoring of polynomial expressions in terms of a, b, c, d by using substitutions to e, f, g, h; expansions to different powers of expressions in terms of a, b, w; expansions of expressions a+b+c+d+e to different powers and assignment of values to different terms.

Identifier

FSUDirac_12_1e_0011

Format

Set of related objects


Title

Expansions and summations of fifthdegree term, with substitution.

Abstract/Description

Assignment of values to different quintic summation expansions in terms of A,B,C,D (similar to FSUDirac_12_1d_0024). Comparison of coefficients of above expansions. Derivation of trigonometric equations from logarithmic equations. Rewriting equations in terms of O,P,Q,R in terms of a,b,r.

Identifier

FSUDirac_12_1e_0018

Format

Set of related objects


Title

Expansions and summations of fifthdegree term, with substitution and comparison of coefficients.

Abstract/Description

Assignment of values to expansions of quintic summations of x and a in terms of a,b,c,d (similar to FSUDirac_12_1d_0024). Comparison of coefficients of above expansions. Assignment of values to expansions of summations of x,a,c (hard to read).

Identifier

FSUDirac_12_1e_0019

Format

Set of related objects


Title

Expansions of terms in third, fourth, and fifthdegree polynomials.

Abstract/Description

Expansions and summations of terms from a quintic polynomial.

Identifier

FSUDirac_12_1e_0014

Format

Set of related objects


Title

Expansions of various powers, with comparison of coefficients.

Abstract/Description

Assignments of values to various expansions of different powers in terms of a, b, c, and sometimes d (similar to FSUDirac_12_1d_0027); chart comparing coefficients to different expansions in terms of ad and with high powers (e.g. 30).

Identifier

FSUDirac_12_1e_0015

Format

Set of related objects


Title

Factors, primes, and remainders (modular arithmetic).

Abstract/Description

Further number theoretical analysis involving factors, primes and remainders using modular arithmetic.

Identifier

FSUDirac_12_1c_0023

Format

Image (JPEG2000)


Title

Fifthdegree polynomial equations.

Abstract/Description

Expansion of x^5 for x = y + z and attempt to rewrite expanded expression in terms of q, r, p, s; expanding general quintic expressions.

Identifier

FSUDirac_12_1e_0013

Format

Set of related objects


Title

Investigating powers, factors, and primes.

Abstract/Description

Number theoretical analysis of factors; Possibly from a succession of problems (number 3 in top right matches numbers in top right of FSUDirac_12_1c_0027 and FSUDirac_12_1c_0028).

Identifier

FSUDirac_12_1c_0034

Format

Image (JPEG2000)


Title

List of permultations of five elements chosen from five: Multiple representations.

Abstract/Description

Listing of permutations of five elements chosen from five (similar to FSUDirac_12_1d_0014).

Identifier

FSUDirac_12_1e_0021

Format

Set of related objects


Title

Logarithmic equations.

Abstract/Description

Possible attempt to solve logarithmic equations.

Identifier

FSUDirac_12_1e_0004

Format

Image (JPEG2000)


Title

Manipulation of fractional expressions.

Abstract/Description

Decomposing fractional expressions involving arbitrary functions (possibly calculus).

Identifier

FSUDirac_12_1a_0015

Format

Image (JPEG2000)


Title

Manipulation of fractional expressions.

Abstract/Description

Continuation of FSUDirac_12_1a_0015 fractional decomposition; Attempts to write fractional expressions in terms of summation and multiplication.

Identifier

FSUDirac_12_1a_0016

Format

Image (JPEG2000)


Title

Manipulations of equations in many variables.

Abstract/Description

Attempt to rearrange equations involving t1 through t4, b, c; Solving matrix equations containing λ (possibly evaluating eigenvalues).

Identifier

FSUDirac_12_1b_0011

Format

Image (JPEG2000)


Title

Manipulations of equations in many variables, doodled on an old school progress report.

Abstract/Description

Attempts to solve for λ in multiple problems; Possible attempt to solve for eigenvalues λ.

Identifier

FSUDirac_12_1b_0012

Format

Image (JPEG2000)


Title

Manipulations of matrices involving four unknowns.

Abstract/Description

Manipulation of matrices containing variables c1 through c4 and attempt to solve resulting equation.

Identifier

FSUDirac_12_1c_0017

Format

Image (JPEG2000)


Title

Manipulations on an equation involving five unknowns.

Abstract/Description

Rearranging equation involving t1, t2, t3, b, and c.

Identifier

FSUDirac_12_1b_0010

Format

Image (JPEG2000)


Title

Manipulations on an equation involving six unknowns.

Abstract/Description

Attempting to solve algebra problems involving variables t1 through t4, b, and c.

Identifier

FSUDirac_12_1b_0006

Format

Image (JPEG2000)


Title

Manipulations on equations involving multiple unknowns.

Abstract/Description

Rearranging equation containing t1, t2, t3 x, y, a, b; rearranging expressions involving p, k, m.

Identifier

FSUDirac_12_1b_0007

Format

Image (JPEG2000)


Title

Matrices and differentiation.

Abstract/Description

Analyzing arbitrarily large matrices using differentiation; Producing equations to describe elements of matrices using differentiation and indices.

Identifier

FSUDirac_12_1c_0021

Format

Image (JPEG2000)


Title

Modular arithmetic.

Abstract/Description

Stating equivalences in modular arithmetic modulo k; Stating values of function f at various point a0 through a4.

Identifier

FSUDirac_12_1c_0020

Format

Image (JPEG2000)


Title

Numbers in terms of exponents n and analysis of expressions modulo λ.

Abstract/Description

Number theoretical analysis; Working with sequence of numbers in terms of exponents n and analyzing expressions modulo λ.

Identifier

FSUDirac_12_1c_0030

Format

Image (JPEG2000)


Title

Observations of primes and factors.

Abstract/Description

Number theoretical analysis; Not trying to solve any particular problem, but making observations about primes and factors of certain expressions.

Identifier

FSUDirac_12_1c_0026

Format

Image (JPEG2000)


Title

Old school problem diagrams.

Abstract/Description

Drawings of shapes and tables; Possibly for assigned physics problems as part of school exercises.

Identifier

FSUDirac_12_3_1_0016

Format

Image (JPEG2000)
Pages