{"id":17834,"date":"2019-10-08T09:26:11","date_gmt":"2019-10-08T16:26:11","guid":{"rendered":"https:\/\/faculty.engineering.asu.edu\/bertsekas\/?page_id=17834"},"modified":"2020-04-16T11:17:57","modified_gmt":"2020-04-16T18:17:57","slug":"ten-simple-rules-for-mathematical-writing","status":"publish","type":"page","link":"https:\/\/faculty.engineering.asu.edu\/bertsekas\/ten-simple-rules-for-mathematical-writing\/","title":{"rendered":"Ten simple rules for mathematical writing"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; _builder_version=&#8221;3.23.3&#8243; background_image=&#8221;https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-content\/uploads\/2019\/07\/shutterstock_160467593-mechanics-bkgd-16&#215;9-hero.jpg&#8221; inner_width_tablet=&#8221;50px&#8221; inner_max_width_tablet=&#8221;50px&#8221; custom_padding=&#8221;0px|0px|0px|0px&#8221; z_index_tablet=&#8221;500&#8243; box_shadow_horizontal_tablet=&#8221;0px&#8221; box_shadow_vertical_tablet=&#8221;0px&#8221; box_shadow_blur_tablet=&#8221;40px&#8221; box_shadow_spread_tablet=&#8221;0px&#8221;][et_pb_row column_structure=&#8221;2_3,1_3&#8243; _builder_version=&#8221;4.4.1&#8243; background_size=&#8221;initial&#8221; background_position=&#8221;top_left&#8221; background_repeat=&#8221;repeat&#8221; custom_padding=&#8221;100px||100px||false|false&#8221;][et_pb_column type=&#8221;2_3&#8243; _builder_version=&#8221;3.0.47&#8243; background_color=&#8221;rgba(0,0,0,0.5)&#8221; custom_padding=&#8221;|||&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_text admin_label=&#8221;Page Title &#8221; _builder_version=&#8221;4.4.1&#8243; background_layout=&#8221;dark&#8221; custom_padding=&#8221;4px|10px|4px|10px&#8221; hover_enabled=&#8221;0&#8243; z_index_tablet=&#8221;500&#8243; text_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; text_text_shadow_vertical_length_tablet=&#8221;0px&#8221; text_text_shadow_blur_strength_tablet=&#8221;1px&#8221; link_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; link_text_shadow_vertical_length_tablet=&#8221;0px&#8221; link_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ul_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ul_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ul_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ol_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ol_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ol_text_shadow_blur_strength_tablet=&#8221;1px&#8221; quote_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; quote_text_shadow_vertical_length_tablet=&#8221;0px&#8221; quote_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_2_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_2_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_2_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_3_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_3_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_3_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_4_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_4_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_4_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_5_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_5_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_5_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_6_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_6_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_6_text_shadow_blur_strength_tablet=&#8221;1px&#8221; box_shadow_horizontal_tablet=&#8221;0px&#8221; box_shadow_vertical_tablet=&#8221;0px&#8221; box_shadow_blur_tablet=&#8221;40px&#8221; box_shadow_spread_tablet=&#8221;0px&#8221;]<\/p>\n<h1>Ten simple rules for mathematical writing<\/h1>\n<p>\u00a0<\/p>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;1_3&#8243; _builder_version=&#8221;3.0.47&#8243; custom_padding=&#8221;|||&#8221; custom_padding__hover=&#8221;|||&#8221;][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=&#8221;1&#8243; _builder_version=&#8221;3.22&#8243;][et_pb_row _builder_version=&#8221;3.25&#8243; background_size=&#8221;initial&#8221; background_position=&#8221;top_left&#8221; background_repeat=&#8221;repeat&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;3.0.47&#8243; custom_padding=&#8221;|||&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_text _builder_version=&#8221;3.27.4&#8243; z_index_tablet=&#8221;500&#8243; text_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; text_text_shadow_vertical_length_tablet=&#8221;0px&#8221; text_text_shadow_blur_strength_tablet=&#8221;1px&#8221; link_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; link_text_shadow_vertical_length_tablet=&#8221;0px&#8221; link_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ul_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ul_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ul_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ol_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ol_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ol_text_shadow_blur_strength_tablet=&#8221;1px&#8221; quote_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; quote_text_shadow_vertical_length_tablet=&#8221;0px&#8221; quote_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_2_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_2_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_2_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_3_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_3_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_3_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_4_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_4_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_4_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_5_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_5_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_5_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_6_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_6_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_6_text_shadow_blur_strength_tablet=&#8221;1px&#8221; box_shadow_horizontal_tablet=&#8221;0px&#8221; box_shadow_vertical_tablet=&#8221;0px&#8221; box_shadow_blur_tablet=&#8221;40px&#8221; box_shadow_spread_tablet=&#8221;0px&#8221;]<\/p>\n<p>Mathematical writing is the type of writing where mathematics is used as a primary means for expression, deduction, or problem solving. It is fundamentally different from creative and expository writing for two main reasons:<\/p>\n<ul>\n<li>it involves the interplay of two languages (natural and math),<\/li>\n<li>it requires much slower reading (it expresses complex ideas that must often be read and pondered several times).<\/li>\n<\/ul>\n<p>As a result, many of the rules and suggestions found in writing style manuals are inadequate and\/or do not apply. We propose an approach to mathematical writing, based on a set of simple composition rules. These rules are outlined in a <a href=\"https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-content\/uploads\/sites\/129\/2019\/10\/ten-rules-for-math-writing.pdf\">slide presentation<\/a> from an April 2002 lecture at MIT (edited later), and focus on the structure of the entire document (the content and the interconnections of different parts):<\/p>\n<p><strong>* Organize in segments<br \/><\/strong><\/p>\n<p><strong>* Write segments linearly<br \/><\/strong><\/p>\n<p><strong>* Consider a hierarchical development<\/strong><\/p>\n<p><strong>* Use consistent notation and nomenclature<br \/><\/strong><\/p>\n<p><strong>* State results consistently<br \/><\/strong><\/p>\n<p><strong>* Don&#8217;t underexplain &#8211; don&#8217;t overexplain<\/strong><\/p>\n<p><strong>* Tell them what you&#8217;ll tell them<br \/><\/strong><\/p>\n<p><strong>* Use suggestive references<br \/><\/strong><\/p>\n<p><strong>* Consider examples and counterexamples<br \/><\/strong><\/p>\n<p><strong>* Use visualization when possible<br \/><\/strong><\/p>\n<p>The <a href=\"https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-content\/uploads\/sites\/129\/2019\/10\/ten-rules-for-math-writing.pdf\">lecture slides<\/a> can be freely downloaded and used for personal or educational purposes.<\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ten simple rules for mathematical writing\u00a0 Mathematical writing is the type of writing where mathematics is used as a primary means for expression, deduction, or problem solving. It is fundamentally different from creative and expository writing for two main reasons:it involves the interplay of two languages (natural and math),it requires much slower reading (it expresses<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"class_list":["post-17834","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-json\/wp\/v2\/pages\/17834","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-json\/wp\/v2\/comments?post=17834"}],"version-history":[{"count":0,"href":"https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-json\/wp\/v2\/pages\/17834\/revisions"}],"wp:attachment":[{"href":"https:\/\/faculty.engineering.asu.edu\/bertsekas\/wp-json\/wp\/v2\/media?parent=17834"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}