An Introduction to Mathematics for Philosophers and Mathematicians.

Sorry for the recent delay (due to inclement weather that one of the instructors had been experiencing) in posting lecture materials. Normal scheduling shall resume soon

This course will cover elementary algebra, geometry, and some aspects of precalculus and calculus, but it shall be approaching these subjects from the perspective of higher mathematics and philosophy of mathematics. The mathematics covered will be at the high school to first year undergraduate level, so people with very little background in mathematics, but an interest in what philosophers and mathematicians do and in learning mathematics should get a lot out of the course. We will introduce some concepts in higher mathematics, including set theory, combinatorics, measure theory, number theory, analysis, proof theory and abstract algebra, and we shall show how the elementary concepts relate to these topics. We will also introduce concepts in the philosophy of mathematics, such as what mathematical objects and relations and properties are (mathematical metaphysics), whether we discover or construct them, and how we know about them (mathematical epistemology), and how to go about mathematics (normative mathematics).

  1. What is a number?

    Make a Khan Academy Account and add me and ange1obear as a coach by clicking on your user name in the top right and adding our email to your "coaches" list (uredditmath@gmail.com). After doing this, watch Kahn Academy's entire Addition and Subtraction series doing all the practice module problems in between (they are the starred items in the side bar). We will not be able to track your progress if you don't do this!

    Try to think about how we might define a number. Also register on the Canvas page so that you can get the first reading.


We are literally starting you at 1+1=2 (per Khan Academy's practice module), so very little mathematical background is required here. The Higher Mathematics and Philosophy is mostly conceptual, but a background in either is helpful (e.g. if you have already taken a mathematics course and are taking this one to brush up, you are in an excellent position to get a lot from the course, ditto if you've taken a philosophy of mathematics course). You will also require adobe acrobat reader or a browser which can read pdfs, and an email so you can use canvas.


There are three aspects to this course. The first is the elementary mathematics (algebra, geometry, precalculus, etc) aspect, which shall consist of mostly third party material (Kahn Academy, other Ureddit courses in introductory mathematics, etc). Each week (and sometimes more than once a week), a lecture shall be presented on a given topic in elementary mathematics, and a problem set/quiz with our selected problems shall appear on the Canvas page for students to do (more on Canvas below). The second aspect of the course is the higher mathematics aspect. We will introduce a higher mathematical concept in a followup lecture which relates to the elementary concept in that week's lecture. We will then assign a problem or two that would be relevant to understanding that concept and how mathematicians use it. The third aspect is the philosophy of mathematics, which shall consist of a reading authored by a philosopher of mathematics on a subject relevant to the higher mathematics concept that week or the lower mathematics one. One or two problems shall be assigned which are relevant to that topic as well. Live conferences shall occasionally be held over Canvas depending on student demand for either review or learning new material in a more discussion based format.

Course Material

Course Texts

The main course texts (which all include available on the internet for free) in each aspect are (abbreviations included after titles):

Elementary Mathematics: Elementary Mathematics by WWL Chen and XT Duong [EM] (this text is mostly supplementary, Khan Academy's practice module and other courses shall be providing most of the material in video, not text, format. Doing as many problems as you can is essential for building your mathematical intuition, so it's good to read these resources for practice problems).

Higher Mathematics: Elements of Abstract and Linear Algebra by Edwin H. Connell [EAA] and William F. Trench's Introduction to Real Analysis [IRA] are available online for students to consult if they wish. The lectures introducing these concepts shall probably be sufficient for you to do the problems assigned on them, and we will not be getting in as deep as these books do, but students who are interested in exploring higher math on a deeper level during this course are encouraged to make use of the "How to Become a Pure Mathematician or Statistician" [HBPMS] blog and the ureddit course on group theory.

Philosophy of Mathematics: Philosophy of Mathematics: Selected Readings by Benacerraf and Putnam [PM] and Russell's An Introduction to Mathematical Philosophy [IMP]. Readings from PM will be posted in the subreddit.

Web Resources

Along with reading material, this course will also include some video and teaching module resources, including:

Canvas: Canvas is a teaching module, similar to blackboard and sakai, which allows instructors to give online quizzes to students, do webconferences, and give and receive assignments as well as update a class. The assignments (e.g. problem sets and quizzes) shall all be posted on canvas (due to its latex functionality) and web conferences shall be done on Canvas. To use the canvas site, you will have to email an instructor your email.

Khan Academy [KA]: We really owe everything to this guy. He's very committed to free information, and his practice module for mathematics (click on "practice" after making an account) is very intuitive and simple. We'll be tracking your progress on this as you go through the course, and using Khan's videos to introduce many elementary mathematics concepts.

"How to Become a Pure Mathematician or Statistician" [HBPMS]: This is an excellent blog for someone wanting to self-study any level of mathematics. Many free resources are included. We will be using material from this site mostly for practice problems.

The Stanford Encyclopedia of Philosophy [SEP]: is the foremost reference in academic philosophy today for a good reason. Each article is written by a notable philosopher on the article's subject, and the non-philosophy stuff isn't bad either (linked here is the introductory article on set theory, which is a very good resource for you to study right now to learn topics on the first part of the course).

The Course Outline

Lower Math portions are denoted by [LM] at the front, higher math portions are denoted by [HM] and Philosophy portions are denoted by [P]

  1. What is a Number?

    • [LM]: Addition, Subtraction, Multiplication, Division, Order of Operations, Fractions, and Exponents.
    • [HM]: Addition is defined, and the arguments it takes (numbers) are questioned as to their appropriate definitions. Set Theory is introduced.
    • [P]: What do we mean when we give a mathematical definition of something? The notion of an axiom and a theorem are fleshed out. Grounding relations are explored and logicism is introduced.
  2. Where are the numbers?

    • TBD
Additional information

The e-mail for reaching either of us is uredditmath@gmail.com

Teacher qualifications

Ange1obear is a graduate student in philosophy at a top 20 department (Leiter) in the US. He has bachelor's degrees in physics and philosophy from a top 5 university (US News). Gnomic is an upperclassman biochemistry major at a university whose Mathematics department is among the top 20 in the US (US News) and whose Philosophy department is among the top 10 (Leiter).

Latest Update


1. nawweba
2. Flipsnory
3. basheesh
4. nipples_r_us
5. agentneuron
6. yunrustin
7. patrick.doc
8. raag3
9. Teach0
10. polarbear122
11. slavalove
12. alishab
13. reeve512
14. misterwhirly89
15. Devilius
16. schmeirik
17. BuckinFullshit
18. OrangeJuice
19. fukitol13
20. kalebwm
21. obsidianight
22. lesbianenemyno1
23. alnapugofa
24. 123nogo
25. jerry_teps
26. Fidelbear
27. AdamMcLean
28. lochinvar
29. drQuirky
30. samadhi
31. sunupradana
32. LadySloth
33. shittymath
34. ZZ9PluralZAlphaTowels
35. Beginner
36. addemf
37. BobKickass
38. When_Nature_Sleeps
39. Malpaso
40. dancory
41. basetw0
42. Glogin
43. orsr
44. Karellen
45. larrylemur
46. bwsullivan
47. fatosholgacher
48. Whomp
49. agtesta
50. aidsy
51. kdevs
52. Void07
53. learnin-stuff
54. sami055
55. Ophashias
56. noeth
57. kenkubus
58. krismacd
59. MovingMoving
60. jetblackswan
61. andiderp
62. mukilan
63. dinosaur_porkchop
64. tamedame
65. dstilwell
66. gavhanna
67. thog
68. jumi99
69. allxk
70. Keekins
71. kbugeja
72. brightbard12-4
73. Faith_In_Chaos
74. SamuraiHelmet
75. mscurlz
76. APasserBy
77. s1cko
78. ikeamoah
79. mattylee
80. rebaru212
81. grant.halsall
82. proteanbeing
83. 6567770
84. steeve149
85. tenoman
86. DIRDept
87. qu3ry
88. faeruss
89. TonyDarko
90. ThePretentiousIlliterate
91. pauq
92. atubofpudding
93. jzm5c
94. khromonkey
95. aoper
96. lytnbb
97. katemccredie1
98. dead_mice_dont_eat
99. duffluff
100. bookmarkjedi
101. Algizz
102. N0tAUsername
103. 109078797
104. AiTueuse
105. Bhane
106. antithesis
107. coolplate
108. theansweris7
109. spencerutt
110. dartharagorn
111. Futurephysicist
112. mr_noda
113. Witten
114. JJTheJetPlane5657
115. nooonecanfindmenow
116. texasranger000
117. ggwhiz
118. LuminalZero
119. TheWizard
120. in_toto
121. Maromi
122. mepat1111
123. qwertykris
124. axeligadoo
125. AmundsenJunior
126. phoenix17
127. Silly_Puddie
128. simple_song
129. smeleanor
130. sanktova
131. fredspeaking
132. theKnightlore
133. garnade31
134. pankratovster
135. charliesherrod4
136. jaredks
137. meltingfishes
138. blackestwolf
139. trevbox
140. BurtandBart
141. preetasaurus
142. ipostawkwardthings
143. bookworm234
144. liutanyu
145. professorfowler
146. bemusedfuse
147. gnuhcikciv
148. rellonaut
149. Colombo
150. Slohmoh
151. ashessnow
152. SolP
153. DerFlieger
154. Feurbach_sock
155. joaco4ever11
156. Trkrtrk
157. Trkrtrk
158. DanielCrook
159. hellavela
160. qzpmwxin
161. microban348
162. mr_oink
163. itogation
164. vitaminz951
165. for_future_refrence
166. helenie.z
167. dstoohey
168. mathematician_
169. MyNameIsRed
170. mathit
171. theSeeker
172. prealekoruz
173. profryan
174. neronexus
175. applesandplums
176. towardsnaturalism
177. behyeefatt
178. Grammr
179. zentropia
180. shalombi
181. jcsoybomb