math tweak check

ch04_keys.adoc

@@ -117,7 +117,7 @@ use to pick that number does not matter as long as it is not predictable
 or repeatable. Bitcoin software uses cryptographically secure random
 number generators to produce 256 bits of entropy.
 
-More precisely, the private key can be any number between 0 and n -
+More precisely, the private key can be any number between 0 and _n_ -
 1 inclusive, where _n_ is a constant (_n_ = 1.1578 × 10^77^, slightly less
 than 2^256^) defined as the order of the elliptic curve used in Bitcoin
 (see <<elliptic_curve>>). To create such a key, we randomly pick a
@@ -343,10 +343,10 @@ find the public key _K_:
 
 [source, python]
 ----
-K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD * G
+K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD × G
 ----
 
-Public key _K_ is defined as a point K = (x, y):
+Public key _K_ is defined as a point _K_ = (_x_, _y_):
 
 [latexmath]
 ++++
@@ -1085,9 +1085,9 @@ The "32" stands for the number of characters in the bech32 alphabet
 .Bech32 typo detection
 ====
 Address:
-  bc1p9nh05ha8wrljf7ru236awpass:[<u>n</u>]4t2x0d5ctkkywm**v**9sclnm4t0av2vgs4k3au7
+  bc1p9nh05ha8wrljf7ru236awpass:[<u><em>n</em></u>]4t2x0d5ctkkywmpass:[<u><em>v</em></u>]9sclnm4t0av2vgs4k3au7
 
-Detected errors shown in bold.  Generated using the
+Detected errors shown in bold and underlined.  Generated using the
 https://oreil.ly/paWIx[bech32 address decoder demo].
 ====
 

ch05_wallets.adoc

@@ -141,7 +141,7 @@ simply adding the same value to both sides of the equation:
 [latexmath]
 ++++
 \begin{equation}
-K + (123 \times G) =\!= (k + 123) \times G
+K + (123 \times G) =\!\!\!= (k + 123) \times G
 \end{equation}
 ++++
 

ch08_signatures.adoc

@@ -845,8 +845,10 @@ Nonlinear::
   significantly slows down operations and which, in some cases, has
   resulted in software accidentally leaking private keys.
 
-Looking at the math of ECDSA,
-signatures are created by a mathematical function _F_~_sig_~
+==== ECDSA Algorithm
+
+Let's look at the math of ECDSA.
+Signatures are created by a mathematical function _F_~_sig_~
 that produces a signature composed of two values.  In ECDSA, those two
 values are _R_ and _s_.
 

ch12_mining.adoc

@@ -858,7 +858,7 @@ is:
 
 ++++
 <ul class="simplelist">
-  <li>target = coefficient * 2<sup>(8*(exponent – 3))</sup></li>
+  <li>target = coefficient × 2<sup>(8 × (exponent – 3))</sup></li>
 </ul>
 ++++
 
@@ -870,7 +870,7 @@ Using that formula, and the difficulty bits value 0x1903a30c, we get:
 </ul>
 ++++
 
-which in decimal is:
+which is:
 
 ++++
 <ul class="simplelist">
@@ -941,7 +941,7 @@ resulting in a retargeting bias toward higher difficulty by 0.05%.
 <<retarget_code>> shows the code used in the Bitcoin Core client.
 
 [[retarget_code]]
-.Retargeting the proof of work—[.plain]#++CalculateNextWorkRequired()++# in pow.cpp
+.Retargeting the proof of work[.plain]#—++CalculateNextWorkRequired()++# in pow.cpp
 ====
 [source,cpp]
 ----

preface.asciidoc

@@ -125,9 +125,11 @@ Watch us on YouTube: link:$$https://youtube.com/oreillymedia$$[].
 
 === Contacting the Authors
 
-[role="align"]
+++++
+<p class="align">
 You can contact Andreas M. Antonopoulos on his personal site:
-[.keep-together]#link:$$https://antonopoulos.com$$[].#
+<span class="keep-together"><a href="https://antonopoulos.com">https://antonopoulos.com</a>.</span></p>
+++++
 
 Follow Andreas on Facebook:
 link:$$https://facebook.com/AndreasMAntonopoulos$$[].